实验流场超分与重建中的双向时间信息利用方法

Human abnormal behavior detection in intelligent surveillance scenarios faces dual challenges: complex spatiotemporal feature coupling and limited edge computing resources. To address these issues, this paper proposes a lightweight and efficient anomaly detection framework, namely the Spatiotemporal Graph Bidirectional Autoencoder (ST-GBAE). This method abandons the conventional computationally intensive RGB pixel-based approaches. Instead, it leverages human skeleton data. Graph Convolutional Networks (GCN) are employed to explicitly model the skeletal topology in non-Euclidean space. Bidirectional Long Short-Term Memory networks (Bi-LSTM) are cascaded to capture global causal dependencies of action sequences along the temporal dimension. The model adopts an unsupervised learning paradigm. It constructs a latent manifold by minimizing the reconstruction error of normal behaviors. Subsequently, unknown anomalies are precisely identified through the reconstruction failure mechanism. Extensive experiments on the ShanghaiTech benchmark dataset demonstrate that ST-GBAE achieves an AUC of 0.965, reaching accuracy levels comparable to state-of-the-art heavy Transformer models. Moreover, with only 1.85 M parameters, it attains a real-time inference speed of 172 FPS, approximately 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document} faster than comparable methods. These results confirm the effectiveness of joint spatiotemporal modeling and establish the significant advantages of this method in balancing accuracy and efficiency. This work provides a valuable solution for deploying large-scale real-time intelligent security systems.

Structural health monitoring (SHM) often suffers from sensor sparsity, making full-field response estimation challenging. We propose a physics-informed spatio-temporal graph network that represents the structure as a complete graph with 34-dimensional node descriptors and 17-dimensional edge attributes. A dual-stream encoder integrates graph attention networks (spatial features) with bidirectional recurrent units (temporal features), followed by cross-attention to propagate information from observed to unobserved nodes. Validated on the IASC-ASCE SHM benchmark with 50% sensor coverage, the model achieves R2 = 0.52 and correlation ρ = 0.73 in the test split, demonstrating consistent reconstruction of dominant structural dynamics under sparse sensing.

Urban traffic, environmental, and utility monitoring systems generate multivariate sensor streams whose spatial relations and missing-data mechanisms evolve over time. This critical narrative review examines graph-based forecasting and reconstruction in the presence of unreliable sensor observations. Foundational diffusion and spatiotemporal graph convolutional models are considered alongside adaptive adjacency learning and bidirectional temporal imputation. The synthesis separates three frequently conflated questions: whether the graph describes physical connectivity, whether it captures statistical dependency, and whether missing entries are informative about the operating state. A protocol is developed for evaluating sensor outages, topology drift, prediction horizons, and leakage from imputation. The review concludes that a missingness-aware architecture must be paired with a missingness-aware test design; otherwise, numerical accuracy may not represent operational performance. The paper offers analytical guidance and a reproducibility checklist, not new model results.

Sensor anomaly detection is essential for reliable condition monitoring in complex equipment. However, existing methods often neglect the independent correlation structures among multiple sensors, resulting in a high misjudgment rate and insufficient robustness. This article addresses issues such as low sensor monitoring reliability and signal distortion in multisensor measurement systems by proposing a method for sensor anomaly detection and measurement signal reconstruction that integrates correlation analysis with spatiotemporal modeling. First, a stable sensor association graph is constructed through partial correlation analysis to identify robust input features. Then, a bidirectional gated recurrent unit (BiGRU)-Transformer model reconstructs the target sensor signal by capturing both local temporal dynamics and global intersensor dependencies. Furthermore, an innovative discriminant method based on multiindex fusion is proposed. It combines reconstruction residuals and partial correlation shift features to achieve sensor anomaly detection. Experiments on real-vehicle monitoring data of vehicle transmission systems show that the proposed method significantly reduces the root-mean-square error (RMSE) in the lubricating oil pressure reconstruction task, with an anomaly discrimination accuracy of 97.89%, significantly outperforming residual-only baselines. This work focuses on sensor data processing and intelligent analysis, providing a new technical solution for intelligent sensing and monitoring.

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Reconstructing fine-grained urban air-pollution fields from sparse monitoring networks is challenging when only a few stations are observed and most of the region is unmeasured. We study an extreme sparse extrapolation setting with four stations and a 456-grid field, and propose Bi-GRIN-Diff, a conditional diffusion model with a bidirectional graph recurrent denoiser for spatiotemporal propagation. We further introduce re-noising clamping to enforce measurement fidelity during reverse sampling by matching the current noise level before clamping, avoiding clean/noisy mismatch. Without grid-level ground truth, we evaluate using re-masked pseudo-missing station entries and qualitative grid snapshots, and show improved reconstruction and probabilistic performance over strong baselines on an Augsburg air-quality dataset.

Time series prediction plays a crucial role in the field of transportation, where it is widely applied in several key areas such as traffic flow analysis and route planning. Most traffic prediction models rely on Mean Squared Error (MSE) as the core metric for training. However, this MSE-based training approach suffers from an issue known as prediction delay. Prediction delay refers to the discrepancy in timing between the predicted results and the actual traffic conditions, which can lead to serious consequences in traffic management. For instance, in urban traffic flow prediction, even if the prediction model has a low MSE value, if the predictions consistently lag behind the actual traffic data, the practical value of such predictions in traffic management would be significantly diminished. Moreover, although deep learning technologies have achieved notable success in time series prediction, most existing research focuses on discrete model frameworks. These frameworks have limitations in capturing deep structural features and effectively aggregating temporal information. Additionally, the sparsity of traffic data poses challenges for more granular prediction tasks. Neural Ordinary Differential Equations (NODEs) have garnered attention in deep learning due to their advantages in simulating dynamic systems and handling time series data. They offer a new perspective for understanding complex systems, particularly in traffic flow prediction, by modeling the dynamic changes of traffic networks as continuous time-evolving processes, effectively capturing the instantaneous changes and long-term trends of traffic flows. To overcome these limitations, researchers are exploring more advanced methods that can more effectively integrate spatiotemporal information, aiming to more accurately understand and predict the complex dynamics in time series and handle continuous-time representations.

Abstract Accurate estimation of missing traffic data is one of the essential components in intelligent transportation systems (ITS). The non-Euclidean data structure and complex missing traffic flow patterns make it challenging to capture nonlinear spatiotemporal correlations of missing traffic flow, which are critical for the imputation of missing traffic data. In this study, we propose a novel multi-view bidirectional spatiotemporal graph network called Multi-BiSTGN to impute urban traffic data with complex missing patterns. First, three spatiotemporal graph sequences are constructed to comprehensively describe traffic conditions from different temporal correlation views, i.e. temporal closeness view, daily periodicity view, and weekly periodicity view. Then, three bidirectional spatiotemporal graph networks are fused by a parametric-matrix-based method to obtain the final imputation results. To train the Multi-BiSTGN model, a novel loss function that considers the interactions between three temporal correlation views is designed to optimize the parameters of the Multi-BiSTGN model. The proposed model was validated on real-world traffic datasets collected in Wuhan, China. Experimental results showed that Multi-BiSTGN outperformed ten existing baselines under different missing types (random missing, block missing, and mixed missing) and missing rates.

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Accurate traffic flow prediction is a key application in Internet of Things (IoT)-enabled intelligent transportation systems (ITSs). However, complex spatiotemporal dependencies and nonstationary anomalies make reliable forecasting particularly challenging. To address these issues, we propose a bidirectional spatiotemporal diffusion graph convolutional network (Bi-STDGCN) with multiscale anomaly-guided attention. The core idea is to jointly model anomaly-aware temporal variations and bidirectional spatial diffusion within a unified multisource dynamic graph framework. First, an anomaly-guided feature enhancement module (AGFEM) employs a difference-driven attention mechanism guided by multiscale temporal patterns derived from wavelet-based decomposition, enhancing the model’s ability to perceive periodic disruptions and sudden traffic fluctuations. Second, Bi-STDGCN captures directional dependencies in both time and space by integrating a bidirectional diffusion dynamic graph convolutional recurrent unit (BDDGCRU) for temporal modeling to reduce prediction lag under anomalies, and a bidirectional diffusion GCN (BD-GCN) to model upstream propagation and downstream feedback patterns in the spatial domain. Third, the multisource dynamic attention-based graph generation (DAGG) incorporates static topology, temporal attributes, real-time traffic states, and hidden node states to construct robust time-varying spatial graphs. Extensive experiments on five real-world datasets demonstrate that Bi-STDGCN achieves state-of-the-art accuracy and robustness, while ablation and visualization analyses further validate the effectiveness of each component.

Temporal dynamic graphs (TDGs), representing the dynamic evolution of entities and their relationships over time with intricate temporal features, are widely used in various real-world domains. Existing methods typically rely on mainstream techniques such as transformers and graph neural networks (GNNs) to capture the spatiotemporal information of TDGs. However, despite their advanced capabilities, these methods often struggle with significant computational complexity and limited ability to capture temporal dynamic contextual relationships. Recently, a new model architecture called mamba has emerged, noted for its capability to capture complex dependencies in sequences while significantly reducing computational complexity. Building on this, we propose a novel method, TDG-mamba, which integrates mamba for TDG learning. TDG-mamba introduces deep semantic spatiotemporal embeddings into the mamba architecture through a specially designed spatiotemporal prior tokenization module (SPTM). Furthermore, to better leverage temporal information differences and enhance the modeling of dynamic changes in graph structures, we separately design a bidirectional mamba and a directed GNN for improved spatiotemporal embedding learning. Link prediction experiments on multiple public datasets demonstrate that our method delivers superior performance, with an average improvement of 5.11% over baseline methods across various settings.

ABSTRACT Existing traffic flow modeling approaches typically rely on real-time observations, such as road sensors or GPS trajectories, which constrain their research scope and application scenarios. This study proposes a novel cross-spatiotemporal graph-based network method to rapidly reconstruct traffic flow speed based on remote sensing images. The method is designed to address the challenges of traffic modeling in the absence of ground observation data. Combining high-resolution remote sensing imagery, vehicle object detection, and graph modeling technology, our approach could handle the discontinuous spatiotemporal graph information. The method incorporates two key modules: a two-layer masked structure mechanism and a cross-spatiotemporal attention computation. This innovative design enables the model to continuously synthesize learning from discontinuous remote sensing images and sparse ground-based sensor data during pre-training, optimizing its parameters and improving prediction accuracy over time. Once pre-trained, the graph model can directly estimate street-level traffic flow speed based solely on remote sensing images. Our results demonstrate state-of-the-art performance (MSE=40.117, MAE=4.768, RMSE=6.334, RSE=0.228), outperforming previous graph-based and sequence-based models. This study showcases the potential of utilizing remote sensing techniques to reconstruct traffic speed in urbanizing regions. It can even be used in scenarios lacking sufficient ground stations and with discontinuous remote sensing data, and enables low-cost, large-scale, and multi-temporal traffic flow speed reconstruction.

As a core function of intelligent transportation systems (ITSs), traffic flow forecasting (TFF) is crucial for reducing congestion in urban areas. Although existing studies have made progress in modeling spatiotemporal dependencies within traffic networks, they ignore the deeper correlations between spatiotemporal features and are particularly deficient in capturing long-distance spatial dependencies and complex dynamic temporal features. To address the aforesaid issues, this paper proposes a Bidirectional Dynamic Spatiotemporal Graph Recurrent Neural Network (Bi-DSTGRNN) for TFF. Specifically, we construct a multi-head self-attention-based gated recurrent unit (MSA-GRU) mechanism to model complex dynamic features of the temporal sequence, utilizing multi-head self-attention to uncover global temporal dependencies, and a bidirectional gated recurrent unit (Bi-GRU) is employed to extract long-term trends. we design a GraphSAGE-based dynamic graph neural network (DGraphSAGE), which dynamically aggregates node features and accurately represents both local and global information in road networks. Finally, we develop a multi-layer Chebyshev graph convolutional network to smooth node embeddings and efficiently extract the global dynamic topology of the traffic network. Experimental results on the PEMSD4 and PEMSD8 datasets demonstrate that the Bi-DSTGRNN model outperforms existing baseline models in prediction accuracy.

When calculating the transient flow around a bridge structure, traditional computational fluid dynamics methods are extremely time-consuming, especially for multiparameter optimization analyses. Inspired by the development of deep graph neural networks with a mesh structure, this paper describes a spatiotemporal prediction framework for the rapid reconstruction and prediction of transient flows on large-scale unstructured grids. To ensure stability and reliability during self-supervised training, a causal self-attention mechanism is employed in the temporal model. The framework is trained and tested on a dataset containing 40 000 snapshots of bridge flow fields with Reynolds numbers ranging from 104 to 105. The relative mean square error of the model in predicting the velocity and pressure fields is found to be in the order of 10−3 and the relative error does not exceed 10%. This demonstrates that the model is capable of reconstructing high-dimensional flow field information from low-dimensional data. Furthermore, the proposed model achieves a computational speedup by two orders of magnitude compared with traditional computational fluid dynamics methods with respect to the temporal inference. To validate its ability to infer bridge aerodynamic characteristics, the model is used to predict the bridge surface pressure, aerodynamic coefficients, streamlines, and vorticity. The results demonstrate that the proposed model has reliable accuracy, representation, and stability in predicting bridge flow fields and identifying multiscale characteristics.

Abstract High-resolution particle image velocimetry (PIV) particle-to-velocity analyses using small interrogation areas (IAs) often require substantial processing time. To overcome this limitation, a generative adversarial network (GAN)-based model is proposed to achieve spatio-temporal super-resolution (SR) reconstruction from low-resolution PIV data with large IAs, thereby significantly reducing post-processing time. Time-resolved PIV measurements of plasma-induced vortex flows, covering vortex formation, growth, transition and breakdown stages, are employed to train and evaluate the model with multi-scale vortical structures. By sequentially constructing spatial and temporal datasets, the GAN-based model enables reliable SR reconstruction at different scaling factors. Reconstruction accuracy is systematically assessed using time-averaged, instantaneous and phase-averaged velocity fields. At SR factors of $\times$ 4 and $\times$ 8, the reconstructed fields closely match high-resolution references, effectively capturing both fluctuating velocities and small-scale vortical structures. In contrast, $\times$ 16 reconstructions exhibit diminished accuracy due to the loss of fine-scale information from highly downsampled inputs. For time-averaged fields, high-resolution reconstructions reliably capture plasma jet characteristics at all SR factors. To enhance generalisation, transfer learning is introduced to fine tune the parameters of SR-related layers in the generator, enabling accurate reconstructions under varying vortex dynamics. In addition, the efficiency gains in PIV particle-to-velocity analysis and the fundamental limitations on achievable SR factors imposed by spatio-temporal data correlations are discussed. This study demonstrates that GAN-based spatio-temporal SR models offer a promising approach to accelerate PIV analyses while maintaining high reconstruction fidelity with diverse flow conditions.

Abstract Velocity measurement techniques, such as particle image velocimetry (PIV), face a trade-off between field of view, spatial resolution and sampling rate, so that small-scale vortices, shear layers and high-frequency turbulent motions are often under-resolved. Most physics-informed reconstructions use a velocity–pressure formulation, even though pressure is not measured in typical PIV experiments, so the Navier–Stokes constraints are only weakly enforced. We address this issue by formulating a vorticity–velocity physics-informed network (VVPINN), in which pressure is eliminated and incompressibility is enforced together with a vorticity transport equation, thereby directly constraining the velocity field and its derivatives. We then compare this formulation with a conventional velocity–pressure PINN (VPPINN) for spatio-temporal super-resolution of planar PIV data in three cases: a laminar multi-cylinder wake, a two-dimensional Taylor–Green vortex and an experimental two-cylinder wake. In the Taylor–Green vortex case, with identical architectures and training strategies, the VVPINN yields smaller velocity errors, reduces the $L_2$ errors in vorticity and shear by approximately $10\,\%$ , and the pressure gradient errors by up to approximately $30\,\%$ at moderate super-resolution factors, and produces instantaneous fields with more physically plausible vorticity, shear and fine-scale pressure gradient patterns. Spectral analysis shows that the temporal energy spectrum is recovered accurately, whereas the wavenumber spectra, particularly beyond the Nyquist wavenumber, remain more difficult to match because the training data strongly constrain the time histories at sampled locations, but only indirectly inform the smallest spatial scales. Overall, the results indicate that vorticity-based constraints provide a more effective route to physics-consistent super-resolution of sub-sampled PIV data than the conventional velocity–pressure formulation.

Particle image velocimetry (PIV) data of high Reynolds number unsteady turbulent flows are often undersampled in time; this leads to aliasing of important spectral content. The present work proposes a novel data-driven estimation technique that uses oversampled sparsely placed surface-mounted pressure sensors and long short-term memory neural networks to resolve the aliased transient velocity dynamics from undersampled PIV data. The method leverages the time-resolved pressure dynamics to estimate the temporal evolution of a proper orthogonal decomposition-based low-dimensional subspace of the velocity field. The proposed approach is demonstrated on a PIV dataset of a high Reynolds number turbulent separated flow over a Gaussian speed-bump benchmark geometry ( $$\text{Re}_{H}=2.26\times 10^{5}$$ Re H = 2.26 × 10 5 , where H is the Bump height). The 15 Hz PIV data is super-resolved to 2 kHz, and spectral analysis of the flowfields is conducted to educe the originally aliased unsteady dynamics of the turbulent separation bubble. The estimator is shown to accurately reconstruct the Reynolds shear stress from unseen sensor data, demonstrating its generalizability to resolve the coherent motions. The estimated velocity spectra show distributions consistent with those of other separated flows.

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As an important technology in ocean engineering and aerospace engineering fields, the development of flow field super-resolution reconstruction technology stems from the urgent need for high-fidelity flow field analysis. In order to avoid the randomness and the difficulty of parameter adjustment caused by machine-learning-based methods for flow field reconstruction, this paper uses the idea of dynamic mode decomposition (DMD), introduces the numerical method Schur–Padé for the real power of the matrix, and proposes a temporal super-resolution flow field prediction method DMD-α, which only uses matrix manipulation to realize the prediction of periodic flow field at any time. Taking the wave field formed by the periodic movement of a trimaran in regular waves as an example, a parameter selection strategy based on the DMD-α method is proposed to take reconstruction accuracy and efficiency into account. Furthermore, proper orthogonal decomposition and Kriging surrogate models are combined to realize the temporal super-resolution flow field prediction for a trimaran with arbitrary side-hull layout to validate the robustness of the DMD-α method. The results show that the proposed DMD-α method is stable, efficient, and can obtain high-fidelity flow prediction, which has great potential in the field of temporal super-resolution prediction of complex flow fields and optimization design based on fluid dynamic performances of various structures.

Most cameras on portable devices adopt a rolling shutter (RS) mechanism, encoding sufficient temporal dynamic information through sequential readouts. This advantage can be exploited to recover a temporal sequence of latent global shutter (GS) images. Existing methods rely on fully supervised learning, necessitating specialized optical devices to collect paired RS-GS images as ground-truth, which is too costly to scale. In this paper, we propose a self-supervised learning framework for the first time to produce a high frame rate GS video from two consecutive RS images, unleashing the potential of RS cameras. Specifically, we first develop the unified warping model of RS2GS and GS2RS, enabling the complement conversions of RS2GS and GS2RS to be incorporated into a uniform network model. Then, based on the cycle consistency constraint, given a triplet of consecutive RS frames, we minimize the discrepancy between the input middle RS frame and its cycle reconstruction, generated by interpolating back from the predicted two intermediate GS frames. Experiments on various benchmarks show that our approach achieves comparable or better performance than state-of-the-art supervised methods while enjoying stronger generalization capabilities. Moreover, our approach makes it possible to recover smooth and distortion-free videos from two adjacent RS frames in the real-world BS-RSC dataset, surpassing prior limitations.

Rolling shutter temporal super-resolution (RSSR), which aims to synthesize intermediate global shutter (GS) video frames between two consecutive rolling shutter (RS) frames, has made remarkable progress with the development of deep convolutional neural networks over the past years. Existing methods cascade multiple separated networks to sequentially estimate intermediate motion fields and synthesize target GS frames. Nevertheless, they are typically complex, do not facilitate the interaction of complementary motion and appearance information, and suffer from problems such as pixel aliasing or poor interpretation. In this paper, we derive the uniform bilateral motion fields for RS-aware backward warping, which endows our network a more explicit geometric meaning by injecting spatio-temporal consistency information through time-offset embedding. More importantly, we develop a unified, single-stage RSSR pipeline to recover the latent GS video in a coarse-to-fine manner. It first extracts pyramid features from given inputs, and then refines the bilateral motion fields together with the anchor frame until generating the desired output. With the help of our proposed bilateral cost volume, which uses the anchor frame as a common reference to model the correlation with two RS frames, the gradually refined anchor frames not only facilitate intermediate motion estimation, but also compensate for contextual details, making additional frame synthesis or refinement networks unnecessary. Meanwhile, an asymmetric bilateral motion model built on top of the symmetric bilateral motion model further improves the generality and adaptability, yielding better GS video reconstruction performance. Extensive quantitative and qualitative experiments on synthetic and real data demonstrate that our method achieves new state-of-the-art results.

Super-resolution (SR) of the degraded and real low-resolution (LR) video remains a challenging problem despite the development of deep learning-based SR models. Most existing state-of-the-art networks focus on getting high-resolution (HR) videos from the corresponding down-sampled LR video but fail in scenarios with noisy or degraded low-resolution video. In this article, a novel real-world “zero-shot” video spatio-temporal SR model, i.e., 3D-Deep Convolutional Auto-Encoder (3D-CAE) guided attention-based deep spatio-temporal back-projection network has been proposed. 3D-CAE is utilized for extracting noise-free features from real low-resolution video and used in the attention-based deep spatio-temporal back-projection network for clean, high-resolution video reconstruction. In the proposed framework, the denoising loss of low-resolution video with high-resolution video reconstruction loss is jointly used in an end-to-end manner with a zero-shot setting. Further, Meta-learning is used to initialize the weights of the proposed model to take advantage of learning on the external dataset with internal learning in a zero-shot environment. To maintain the temporal coherency, we have used the Motion Compensation Transformer (MCT) for motion estimation and the Sub-Pixel Motion Compensation (SPMC) layer for motion compensation. We have evaluated the performance of our proposed model on REDS and Vid4 Dataset. The PSNR value of our model is 25.13 dB for the RealVSR dataset, which is 0.72 dB more than the next-best performing model, EAVSR+. For MVSR4x, our model provides 24.61 db PSNR, 0.67 dB more than the EAVSR+ model. Experimental results demonstrate the effectiveness of the proposed framework on degraded and noisy real low-resolution video compared to the existing methods. Furthermore, an ablation study has been conducted to highlight the contribution of 3D-CAE and attention layer to the overall network performance.

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4D Flow Magnetic Resonance Imaging (4D Flow MRI) is a non-invasive technique for volumetric, time-resolved blood flow quantification. However, apparent trade-offs between acquisition time, image noise, and resolution limit clinical applicability. In particular, in regions of highly transient flow, coarse temporal resolution can hinder accurate capture of physiologically relevant flow variations. Deep learning-based post-processing techniques have shown promise in overcoming these issues using so-called super-resolution networks. However, while existing super-resolution research has primarily focused on spatial upsampling, temporal super-resolution remains largely unexplored. The aim of this study was therefore to implement and evaluate a residual data-driven network for temporal super-resolution 4D Flow MRI. To achieve this, an existing spatial network (4DFlowNet) was re-designed for temporal upsampling, adapting input dimensions, and optimizing internal layer structures. The model was trained and tested on synthetic 4D Flow MRI data derived from patient-specific in-silico models, followed by additional evaluation on clinically acquired in-vivo datasets. Overall, excellent performance was achieved with input velocities effectively denoised and temporally upsampled, with a mean absolute error (MAE) of 1.0 cm/s in an unseen in-silico setting, outperforming deterministic alternatives (linear interpolation MAE = 2.3 cm/s, sinc interpolation MAE = 2.6 cm/s). Further, the network synthesized high-resolution temporal information from unseen low-resolution in-vivo data, with strong correlation observed at peak flow frames. As such, our results highlight the potential of utilizing data-driven neural networks for temporal super-resolution 4D Flow MRI, enabling high-frame-rate flow quantification without extending acquisition times beyond clinically acceptable limits.

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We present TSR-VFD, a novel deep learning solution that recovers temporal super-resolution (TSR) of three-dimensional vector field data (VFD) for unsteady flow. In scientific visualization, TSR-VFD is the first work that leverages deep neural nets to interpolate intermediate vector fields from temporally sparsely sampled unsteady vector fields. The core of TSR-VFD lies in using two networks: InterpolationNet and MaskNet, that process the vector components of different scales from sampled vector fields as input and jointly output synthesized intermediate vector fields. To demonstrate our approach’s effectiveness, we report qualitative and quantitative results with several data sets and compare TSR-VFD against vector field interpolation using linear interpolation (LERP), generative adversarial network (GAN), and recurrent neural network (RNN). In addition, we compare TSR-VFD with a lossy compression (LC) scheme. Finally, we conduct a comprehensive study to evaluate critical parameter settings and network designs.

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Video Super-Resolution (VSR) is the task of reconstructing high-resolution (HR) video sequences from low-resolution (LR) video sequences. Apart from spatial information of reference frames, temporal information of neighboring frames is also important for reconstruction. Current VSR methods usually take advantage of the temporal information through optical flow estimation and compensation. However, optical flow estimation is often inaccurate and difficult, which may result in artifacts or blurring in the reconstructed frames. In this paper, we propose a Novel Flow-guided Deformable Alignment Module (NFDAM) for frame alignment. In this module, a lightweight optical network FNet is designed to estimate optical flow as a coarse offset, which then guides the deformable convolution at the feature and image level. On this basis, we propose a Flow-guided Gated Bidirectional Recurrent Separated Network (FGBRSN) for VSR, in which a gated recurrent structure is designed to leverage long-term information and a multilevel residual fusion approach is used in upsampling module. Our experiments on public datasets have shown that the proposed method improves both quantitative evaluation and visual effects compared with the existing methods.

We propose spatiotemporal deep neural networks for the time-resolved reconstruction of the velocity field around a circular cylinder (DeepTRNet) based only on two flow data types: the non-time-resolved wake velocity field and sparse time-resolved velocity measurements at specific discrete points. The DeepTRNet consists of two operations, i.e., compact spatial representations extraction and sequential learning. We use the convolutional autoencoder (CAE) in DeepTRNet to extract compact spatial representations embedded in the non-time-resolved velocity field. The nonlinear CAE modes and corresponding CAE coefficients are thus obtained. Based on the nonlinear correlation analysis of the velocity field, we use the bidirectional recurrent neural networks (RNN) with the gated recurrent unit for mapping the sparse time-resolved velocity measurements to the CAE coefficients via sequential learning. The early stopping technique is used to train the DeepTRNet to avoid overfitting. With the well-trained DeepTRNet, we can reconstruct the time-resolved velocity field around the circular cylinder. The DeepTRNet is verified on the simulated datasets at two representative Reynolds numbers, 200 and 500, and the experimental dataset at Reynolds number 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. We systematically compare the DeepTRNet method and the RNN-proper orthogonal decomposition (POD) approach. The DeepTRNet can obtain the accurate time-resolved velocity field depending on the two data types mentioned above. The DeepTRNet method outperforms the RNN-POD method in the reconstruction accuracy, especially for the reconstruction of small-scale flow structures. In addition, we get the reliable velocity field even for the high-frequency components.

Deep learning methods have recently shown significant promise in compressing the geometric features of point clouds. However, challenges arise when consecutive point clouds contain holes, resulting in incomplete information that complicates motion estimation. To our knowledge, most existing dynamic point cloud compression methods have largely overlooked this critical issue. Moreover, these methods typically employ a multi-scale single-pass approach for motion estimation, performing only one estimation at each scale. This limits accuracy and adversely impacts compression performance. To address these challenges, we propose a dynamic point cloud compression model called M2BR-DPCC (Multi-Modal Multi-Scale Bidirectional Recursion for Dynamic Point Cloud Compression). Our method introduces two key innovations. First, we integrate both point cloud and image data as inputs, leveraging a multi-modal feature representation completion (MFRepC) approach to align information across modalities. This addresses the issue of missing data in point clouds by using complementary information from images. Second, we implement a multi-scale bidirectional recursive (MSBR) motion estimation method. This module iteratively refines motion flows in both forward and backward directions, progressively enhancing point cloud features and improving motion estimation accuracy. Experimental results on widely used datasets, including MVUB and 8iVFB, demonstrate the effectiveness of our approach. Compared to existing methods, M2BR-DPCC achieves superior performance, with an average BD-rate improvement of 95.23% over V-PCC, 12.92% over D-DPCC, and 16.16% over patchDPCC. These results underscore the potential of leveraging multi-modal data and bidirectional refinement for dynamic point cloud compression.

Geophysical logging plays a very important role in reservoir evaluation. In the actual production process, some logging data are often missing due to well wall collapse and instrument failure. Therefore, this paper proposes a logging reconstruction method based on improved sand cat swarm optimization (ISCSO) and a temporal convolutional network (TCN) and bidirectional gated recurrent unit network with attention mechanism (BiGRU-AM). The ISCSO-TCN-BiGRU-AM can process both past and future states efficiently, thereby extracting valuable deterioration information from logging data. Firstly, the sand cat swarm optimization (SCSO) improved by the variable spiral strategy and sparrow warning mechanism is introduced. Secondly, the ISCSO’s performance is evaluated using the CEC–2022 functions and the Wilcoxon test, and the findings demonstrate that the ISCSO outperforms the rival algorithms. Finally, the logging reconstruction method based on the ISCSO-TCN-BiGRU-AM is obtained. The results are compared with the competing models, including the back propagation neural network (BPNN), GRU, and BiGRU-AM. The results show that the ISCSO-TCN-BiGRU-AM has the best performance, which verifies its high accuracy and feasibility for the missing logging reconstruction.

Scene flow estimation provides the fundamental motion perception of a dynamic scene, which is of practical importance in many computer vision applications. In this paper, we propose a novel multi-scale bidirectional recurrent architecture that iteratively optimizes the coarse-tofine scene flow estimation. In each resolution scale of estimation, a novel bidirectional gated recurrent unit is proposed to bidirectionally and iteratively augment point features and produce progressively optimized scene flow. The optimization of each iteration is integrated with the hybrid correlation that captures not only local correlation but also semantic correlation for more accurate estimation. Experimental results indicate that our proposed architecture significantly outperforms the existing state-of-theart approaches on both FlyingThings3D and KITTI benchmarks while maintaining superior time efficiency. Codes and pre-trained models are publicly available at https://github.com/cwc1260/MSBRN.

In underwater reconnaissance and patrol, AUV has to sense and judge traversability in cluttered areas that include reefs, cliffs, and seabed infrastructure. A narrow sonar field of view, occlusion, and current-driven disturbances leave the vehicle with local, time-varying information, so decisions are made with incomplete and uncertain observations. A path-planning framework is built around two coupled components: spatiotemporal graph neural network prediction and conditional normalizing flow (CNF)-based probabilistic environment reconstruction. Forward-looking sonar and inertial navigation system (INS) measurements are fused online to form a local environment graph with temporal encoding. Cross-temporal message passing captures how occupancy and maneuver patterns evolve, which supports path prediction under dynamic reachability and collision-avoidance constraints. For regions that remain unobserved, CNF performs conditional generation from the available local observations, producing probabilistic completion and an explicit uncertainty output. Conformal calibration then maps model confidence to credible intervals with controlled miscoverage, giving a consistent probabilistic interface for risk budgeting. To keep pace with ocean currents and moving targets, edge weights and graph connectivity are updated online as new observations arrive. Compared with Informed Random Tree star (RRT*), D* Lite, Soft Actor-Critic (SAC), and Graph Neural Network-Probabilistic Roadmap (GNN-PRM), the proposed method achieves a near 100% success rate at 20% occlusion and maintains about an 80% success rate even under 70% occlusion. In dynamic obstacle scenarios, it yields about a 4% collision rate at low speeds and keeps the collision rate below 20% when obstacle speed increases to 3 m/s. Ablation studies further demonstrate that temporal modeling improves success rate by about 7.1%, CNF-based probabilistic completion boosts success rate by about 13.2% and reduces collisions by about 17%, while conformal calibration reduces coverage error by about 6.6%, confirming robust planning under heavy occlusion and time-varying uncertainty.

The reconstruction of high-fidelity flow fields from low-fidelity data has attracted considerable attention in fluid dynamics but poses many challenges to existing deep learning methods due to the spatiotemporal complexity of flows and the lack of standardized benchmark datasets. In this study, we generate a low- and high-fidelity dataset containing 25 600 snapshots of four representative flow dynamics simulations using eight different numerical-precision and grid-resolution configurations. Using this dataset, we develop a physics-guided transformer-based generative adversarial network (PgTransGAN) for concurrently handling numerical-precision and grid-resolution enhancement. PgTransGAN leverages a dual-discriminator-based generative adversarial network for capturing continuous spatial and temporal dynamics of flows and applies a soft-constraint approach to enforce physical consistency in the reconstructed data using gradient information. An efficient transformer model is also developed to obtain the long-term temporal dependencies and further alleviate storage constraints. We compare the performance of PgTransGAN against standard linear interpolation and solutions based solely on convolutional neural networks or generative adversarial networks, and demonstrate that our method achieves better reconstruction quality at the data, image, and physics levels with an upscaling factor of 4 or even 8 in each grid dimension.

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Traffic state reconstruction gets more and more attention for various important applications such as traffic optimization, traffic control, and congestion avoidance. There exist several approaches to detect traffic parameters like speed, flow, and density. A quite common approach in the past was to use stationary detectors like induction loops. An emerging technology is to handle traffic state by floating-car data (probe vehicles) with a high resolution of time and location measurements via GPS. A third methodology is to detect vehicles using the recognition of in-use Bluetooth devices and to derive an average travel time between two Bluetooth detectors. For the first two approaches, several traffic state reconstruction methods exist. This paper aims at reconstructing the prevailing traffic situation out of low-resolution travel times based on Bluetooth captions. A methodology is developed on how to reconstruct the traffic speed and is applied to three months of data from a German autobahn equipped with Bluetooth detectors.

Video super resolution aims to recover high resolution frames from multiple low resolution ones. Compared to single frame super resolution, the main challenge of video super resolution is how to effectively utilize the spatiotemporal information in video sequences. Due to inaccurate alignment of information between frames, the reconstruction results often suffer from motion blur and artifacts, which will accumulate during the propagation process and seriously affect the reconstruction quality and continuity of the video. To solve this issue, this paper proposes a Multi-Flow Guided Deformable Alignment module(MFGDA) based on a bidirectional propagation network. This module combines the multi-optical flow information of neighboring frames with deformable convolution, accurately aligns features through bidirectional information propagation, and eliminates artifacts. In addition, to better utilize spatiotemporal information, we also design a Temporal-Spatial Feature Fusion Module (TSFM) based on an attention mechanism. This module mines the spatiotemporal information of features at different time steps, eliminates the alignment errors that occur during long-term information propagation, and enhances the fusion of key features. The experimental results demonstrate that our proposed method achieves superior performance compared with state-of-the-art methods.

Electrical resistance tomography (ERT) has been considered as a data collection and image reconstruction method in many multi-phase flow application areas due to its advantages of high speed, low cost and being non-invasive. In order to improve the quality of the reconstructed images, the Total Variation algorithm attracts abundant attention due to its ability to solve large piecewise and discontinuous conductivity distributions. In industrial processing tomography (IPT), techniques such as ERT have been used to extract important flow measurement information. For a moving object inside a pipe, a velocity profile can be calculated from the cross correlation between signals generated from ERT sensors. Many previous studies have used two sets of 2D ERT measurements based on pixel-pixel cross correlation, which requires two ERT systems. In this paper, a method for carrying out flow velocity measurement using a single ERT system is proposed. A novel spatiotemporal total variation regularization approach is utilised to exploit sparsity both in space and time in 4D, and a voxel-voxel cross correlation method is adopted for measurement of flow profile. Result shows that the velocity profile can be calculated with a single ERT system and that the volume fraction and movement can be monitored using the proposed method. Both semi-dynamic experimental and static simulation studies verify the suitability of the proposed method. For in plane velocity profile, a 3D image based on temporal 2D images produces velocity profile with accuracy of less than 1% error and a 4D image for 3D velocity profiling shows an error of 4%.

Recently, various compressed video quality enhancement technologies have been proposed to overcome the visual artifacts. Most existing methods are based on optical flow or deformable alignment to explore the spatiotemporal information across frames. However, inaccurate motion estimation and training instability of deformable convolution would be detrimental to the reconstruction performance. In this paper, we design a bi-directional recurrent network equipping with enhanced deformable alignment and attention-guided aggregation to promote information flows among frames. For the alignment, a pair of scale and shift parameters are learned to modulate optical flows into new offsets for deformable convolution. Furthermore, an attention aggregation strategy oriented at preference is designed for temporal information fusion. The strategy synthesizes global information of inputs to modulate features for effective fusion. Extensive experiments have proved that the proposed method achieves great performance in terms of quantitative performance and qualitative effect.

Pressure reconstruction from velocity measurements using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) has drawn significant attention as it can provide instantaneous pressure fields without altering the flow. Previous studies have found that the accuracy of the calcualted pressure field depends on several factors including the accuarcy of the velocity measurement, the spatiotemporal resolutions, the method for calculating pressure-gradient, the algorithm for pressure-gradient integration, the pressure boundary condition, etc. Therefore, it is critical and challenging to quantify the uncertainty of the reconstructed pressure field. The recent development of the uncertainty quantification algorithms for PIV and PTV allows for the local and instantaneous uncertainty estimation of velocity measurement, which can be used to infer the pressure uncertainty. In this study, we introduce a framework that propagates the standard velocity uncertainty defined as the standard deviation of the velocity error distribution through the pressure reconstruction process to obtain the uncertainty of the pressure field. The uncertainty propagations through the calculation of the pressure-gradient and the pressure-gradient integration were modeled as linear transformations, which can reproduce the effects of the spatiotemporal resolutions, the numerical schemes, the integration algorithms, and the pressure boundary condition on the accuracy of the resulting pressure fields. The proposed uncertainty estimation approach also considers the effect of the spatiotemporal and componentwise correlation of the velocity errors in common PIV/PTV measurements on the pressure uncertainty.

This paper explores the application of Physics-Informed Neural Networks (PINN) in reconstructing the wake flow of a propeller. Computational Fluid Dynamics (CFD) simulations of the KVLCC2 propeller under open-water conditions are conducted to generate flow field data, which serves as the primary training dataset for the PINN model. A mixed-variable formulation is introduced to formulate and solve the Navier-Stokes (N-S) equations. In traditional Navier-Stokes solvers, high-order derivatives introduce significant computational complexity. By incorporating the Cauchy stress tensor, the reliance on these higher-order derivatives is reduced, which improves the stability of automatic differentiation. The effectiveness of this approach in wake flow reconstruction is evaluated. The results show that the mixed-variable PINN improves the convergence rate and demonstrates strong applicability to propeller flow field prediction and reconstruction.

No abstract available

In the realm of experimental fluid mechanics, accurately reconstructing high-resolution flow fields is notably challenging due to often sparse and incomplete data across time and space domains. This is exacerbated by the limitations of current experimental tools and methods, which leave critical areas without measurable data. This research suggests a feasible solution to this problem by employing an inverse physics-informed neural network (PINN) to merge available sparse data with physical laws. The method's efficacy is demonstrated using flow around a cylinder as a case study, with three distinct training sets. One was the sparse velocity data from a domain, and the other two datasets were limited velocity data obtained from the domain boundaries and sensors around the cylinder wall. The coefficient of determination (R2) coefficient and mean squared error (RMSE) metrics, indicative of model performance, have been determined for the velocity components of all models. For the 28 sensors model, the R2 value stands at 0.996 with an associated RMSE of 0.0251 for the u component, while for the v component, the R2 value registers at 0.969, accompanied by an RMSE of 0.0169. The outcomes indicate that the method can successfully recreate the actual velocity field with considerable precision with more than 28 sensors around the cylinder, highlighting PINN's potential as an effective data assimilation technique for experimental fluid mechanics.

Aiming at the technical challenge of reconstructing high-resolution flow fields from sparse flow field data, research on flow field reconstruction based on the physics-informed neural network (PINN) for underwater vehicles has been carried out. To begin with, the Lattice Boltzmann Method (LBM) was used to construct the benchmark flow field data (Timesequenced velocity and pressure fields in three-dimensional space) of the SUBOFF model, and the sparse flow field dataset is generated by spatial down-sampling of the benchmark flow field data. Subsequently, the fully data-driven algorithm and the PINN deep learning algorithm for SUBOFF flow reconstruction (with spatio-temporal coordinate points as inputs and velocity and pressure fields as outputs) were developed, the fully data-driven model and the PINN were obtained by training with the sparse flow data set. Eventually, only the spatiotemporal coordinate points from the benchmark flow field data were input into the two models, and the complete flow field was reconstructed using model inference inversion, and the results were compared and analyzed with the benchmark flow field data generated by the LBM, to validate the correctness of the reconstructed flow field for the two models. The results demonstrate that the PINN model is significantly more accurate than the fully data-driven model in reconstructing the flow field from sparse flow field data. The study provides a new flow field reconstruction solution that could contribute to the optimal design of the hydrodynamic performance of underwater vehicles and similar structures.

Previous studies have demonstrated that the Ensemble Kalman Filter (EnKF) has been successfully applied to optimize turbulence model constants under various flow conditions, particularly in two-dimensional cases. However, in engineering applications, the flow fields are often three-dimensional and highly nonlinear. Under such conditions, due to the non-uniqueness of the optimal solution in the inverse problem, directly applying the conventional EnKF often yields unsatisfactory results. To address this challenge, this study combines proper orthogonal decomposition (POD) with EnKF to develop a POD-reduced EnKF algorithm for data assimilation in complex three-dimensional flow fields of high-speed trains. By extracting flow field characteristics through POD, the number of observation points is reduced, which significantly enhances the data assimilation accuracy. Results show that the assimilated turbulence model constants lead to good agreement between simulation and experimental data for a high-speed train operating in open-air conditions. The method also demonstrates strong robustness, achieving consistent assimilation performance across different numbers and locations of observation points. In addition, the optimized constants exhibit a certain degree of generalizability, improving prediction accuracy across different inflow conditions and geometries. The proposed framework offers a promising strategy for enhancing aerodynamic modeling of high-speed trains.

Within the framework of the European Union Horizon 2020 project HOMER (Holistic Optical Metrology for Aero-Elastic Research), data assimilation (DA) algorithms for dense flow field reconstructions developed by different research teams, hereafter referred to as the participants, were comparatively assessed. The assessment is performed using a synthetic database that reproduces the turbulent flow in the wake of a cylinder in ground effect, placed at the distance of one diameter from a lower wall. Downstream of the cylinder, this wall continues either in the form of a flat steady wall, or of a flexible panel undergoing periodic oscillations; these two situations correspond to two different test cases, the latter being introduced to extend the evaluation to fluid–structure interaction problems. The input data for the data assimilation algorithms were datasets containing the particle locations and their trajectories identification numbers, at increasing tracer concentrations from 0.04 to 1.4 particles/mm3 (equivalent image density values between 0.005 and 0.16 particles per pixel, ppp). The outputs of the DA algorithms considered for the assessment were the three components of the velocity, the nine components of the velocity gradient tensor and the static pressure, defined in the flow field on a Cartesian grid, as well as the static pressure on the wall surface, and its position in the deformable wall case. The results were analysed in terms of errors of the output quantities with respect to the ground-truth values and their distributions. Additionally, the performances of the different DA algorithms were compared with that of a standard linear interpolation approach. The velocity errors were found in the range between 3 and 11% of the bulk velocity; furthermore, the use of the DA algorithms enabled an increase of the measurement spatial resolution by a factor between 3 and 4. The errors of the velocity gradients were of the order of 10–15% of the peak vorticity magnitude. Accurate pressure reconstruction was achieved in the flow field, whereas the evaluation of the surface pressure revealed more challenging. As expected, lower errors were obtained for increasing seeding concentration. The difference of accuracy among the results of the different data assimilation algorithms was noticeable especially for the pressure field and the compliance with governing equations of fluid motion, and in particular mass conservation. The analysis of the flexible panel test case showed that the panel position could be reconstructed with micrometric accuracy, rather independently of the data assimilation algorithm and the seeding concentration. The accurate evaluation of the static pressure field and of the surface pressure proved to be a challenge, with typical errors between 3 and 20% of the free-stream dynamic pressure.

No abstract available

Accurate prediction of flow and temperature fields within aero engine turbine passages are vital for optimizing engine performance. However, getting complete high-resolution datasets is challenging because of the limits of experimental measurements and the high cost of numerical simulations, such as computational fluid dynamics (CFD). Experimental methods often lead to incomplete data, while high-precision CFD simulations are costly in computation. Data assimilation methods that mix experimental and CFD simulation data can address missing data issues but lose accuracy when significant data proportions are absent. This study introduces a multiple fusion data assimilation method based on proper orthogonal decomposition (POD) to overcome these problems. The approach includes three key advancements: (1) an enhanced mode filtering strategy for improved reconstruction accuracy, (2) embedding physical constraints into the fusion process, and (3) a multistep reconstruction framework that iteratively restores missing data. The method was validated on turbine passage velocity fields and blade surface temperature fields. For the velocity field with 84% missing data, it achieved 95% accuracy over 81.9% of the rebuilt area, surpassing classic POD-based methods by 12.2%. For the temperature field with 91% missing data, it attained 97% accuracy over 89.42% of the rebuilt area, representing a 28.03% improvement over existing methods.

No abstract available

State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface observations. Directly implementing an ensemble Kalman filter based on the full forecast model is usually expensive. One widely used method in practice projects the information of the observed layer to other layers via linear regression. However, large errors appear when nonlinearity in the highly turbulent flow field becomes dominant. In this paper, we develop a multi-step nonlinear data assimilation method that involves the sequential application of nonlinear assimilation steps across layers. Unlike traditional linear regression approaches, a conditional Gaussian nonlinear system is adopted as the approximate forecast model to characterize the nonlinear dependence between adjacent layers. At each step, samples drawn from the posterior of the current layer are treated as pseudo-observations for the next layer. Each sample is assimilated using analytic formulae for the posterior mean and covariance. The resulting Gaussian posteriors are then aggregated into a Gaussian mixture. Therefore, the method can capture strongly turbulent features, particularly intermittency and extreme events, and more accurately quantify the inherent uncertainty. Applications to the two-layer quasi-geostrophic system with Lagrangian data assimilation demonstrate that the multi-step method outperforms the one-step method, particularly as the tracer number and ensemble size increase. Results also show that the multi-step CGDA is particularly effective for assimilating frequent, high-accuracy observations, which are scenarios where traditional EnKF methods may suffer from catastrophic filter divergence.

Abstract A data assimilation (DA) strategy based on an ensemble Kalman filter (EnKF) is used to enhance the predictive capabilities of scale-resolving numerical tools for the analysis of flows exhibiting cyclic behaviour. More precisely, an ensemble of numerical runs using large-eddy simulations (LES) for a compressible intake flow rig is augmented via the integration of high-fidelity data. This observation is in the form of instantaneous velocity measurements, which are sampled at localised sensors in the physical domain. Two objectives are targeted. The first objective is the calibration of an unsteady inlet condition suitable to capture the cyclic flow investigated. The second objective is the analysis of the synchronisation of the LES velocity field with the available observations. In order to reduce the computational costs required for this analysis, a hyper-localisation procedure (HLEnKF) is proposed and integrated in the library CONES, tailored to perform fast online DA. The proposed strategy performs a satisfactory calibration of the inlet conditions, and its robustness is assessed using two different prior distributions for the free parameters optimised in this task. The DA state estimation is efficient in obtaining accurate local synchronisation of the inferred velocity fields with the observed data. The modal analysis of the kinetic energy field provides additional insight into the improved reconstruction quality of the velocity field. Thus, the HLEnKF shows promising features for the calibration and synchronisation of scale-resolved turbulent flows, opening perspectives of applications for complex phenomena using advanced tools such as digital twins.

No abstract available

No abstract available

Fluid dynamics is governed by partial differential equations (PDEs) which are solved numerically. The limitations of traditional methods in data assimilation hinder their effective engagement with experiments. Physics-informed neural network (PINN) has emerged as a hybrid data-physics-driven model for convective problems. However, the approach suffers from low accuracy and poor efficiency due to the way of incorporating PDEs. In this work, a novel convolutional neural network framework integrating finite volume method (FVM) is developed to address the challenge. The interface variables of the grid are predicted by the neural network for the first time, rather than a complex procedure in FVM. The physical law is then learned by minimizing the residual of the discretized conservative form of PDEs. A comparison between this model and the original PINN regarding prediction accuracy demonstrates the superiority of embedding PDEs through FVM. The effects of sampling strategies and quantities are studied. The result confirms the model’s capability to utilize sparsely available internal measurement data. Furthermore, the model performs well even in scenarios where partial initial and boundary conditions are absent.

No abstract available

Efficiently predicting high-resolution and accurate flow fields through networked autonomous marine vehicles (AMVs) is crucial for diverse applications. Nonetheless, a research gap exists in the seamless integration of data-driven flow modeling, real-time data assimilation from flow sensing, and the optimization of AMVs’ sensing strategies, culminating in a closed-loop dynamic data-driven application system (DDDAS). This article presents a novel DDDAS that systematically integrates flow modeling, data assimilation, and adaptive flow sensing using networked AMVs. It features a hybrid data-driven flow model, uniting a neural network for trend prediction and a Gaussian process model for residual fitting. The neural network architecture is designed using knowledge extracted from historic flow data through tidal harmonic analysis, enhancing its capability in flow prediction. The Kriged ensemble transform Kalman filter is introduced to assimilate spatially correlated flow-sensing data from AMVs, enabling effective model learning and accurate spatiotemporal flow prediction, while forming the basis for optimizing AMVs’ flow-sensing paths. A receding horizon strategy is proposed to implement non-myopic optimal path planning, and a distributed strategy of implementing Monte Carlo tree search is proposed to solve the resulting large-scale tree searching-based optimization problem. Computer simulations, employing underwater gliders as sensing networks, demonstrate the effectiveness of the proposed DDDAS in predicting depth-averaged flow in nearshore ocean environments.

No abstract available

ABSTRACT The objective of this study is to obtain accurate flow field analysis results in a short computational time by using data assimilation, which increases the accuracy of Reynolds averaged Navier-Stokes (RANS) simulations with low grid resolution. The large-eddy simulation (LES) results are assimilated into RANS simulations. In those simulations, the turbulence-model parameters are optimised by an ensemble Kalman filter with a proposed method for adaptive hyperparameter optimisation. The target of calculations is the flow field around a square cylinder of the Reynolds number of approximately . Only the surface pressure of the square cylinder is used as an observation variable. For this shape, the assimilated RANS flow field is similar to that given by the LES analysis, and the drag coefficient reproducibility is improved by . The turbulence-model parameters are also used in the analyses of different cross-sectional shape and are found to improve the reproducibility of the flow field.

Recently, there has been a growing demand for flow-based video frame interpolation methods, which introduce correlation volumes to supervise the correlation of bidirectional optical flows. However, they often overlook the symmetry of the bidirectional motion field by consuming substantial computational cost, which is reflected in the fact that these methods often require a long runtime. To address these issues, in this article, we propose a bidirectional 3D correlation volume which is suitable for video frame interpolation. By decomposing the 4D correlation volume into two 3D correlation volumes in the horizontal and vertical directions, we significantly enhance the model’s inference speed with a minor sacrifice compared to our baseline. Additionally, when handling 2K video frames, our method achieves several-fold improvement in inference speed compared to other methods which implied correlation volume. The code is available at https://github.com/famt0531.

Video Frame Interpolation (VFI) is a technique that enhances video quality by generating new frames between adjacent video frames. However, many existing VFI methods exhibit suboptimal performance when dealing with scenes involving complex backgrounds and significant motion. In this paper, we propose an innovative VFI approach named BEOUNet to address these challenges. The model adopts a bidirectional encoding structure to comprehensively capture motion and contextual information between video frames. Furthermore, we introduce depthwise over-parameterized recurrent residual convolutional units (DO-RRCUs) and Convolutional Block Attention Module (CBAM) to optimize the U-Net architecture, thereby enhancing performance while reducing computational complexity. Finally, a multi-scale frame synthesis network is employed to generate interpolated frames. We conduct benchmark tests on various datasets, and experimental results demonstrate its excellent performance in terms of efficiency and quality.

No abstract available

Video frame interpolation can enhance the frame rate and improve video quality by synthesizing non-existing intermediate frames between two consecutive frames. Recently, remarkable advances have been made due to the employment of convolutional neural networks. However, most existing methods suffer from motion blur and artifacts when handling the case of large motion and occlusion. To solve the problem, we propose a lightweight but effective deep neural network which is trained end-to-end. Specifically, the bidirectional attention module is first devised to enhance motion-related features representation in both channel and spatial dimensions. Then the synthesis network estimates kernel weights, visibility map and offset vectors to finally generate the interpolation results. Moreover, to compress the model, we introduce the Ghost module to the synthesis network which is verified to be highly effective. Experiment results demonstrate that our proposed architecture performs favorably against state-of-the-art frame interpolation methods on various public video datasets.

Video frame interpolation (VFI) is of great importance for many video applications, yet it is still challenging even in the era of deep learning. Some existing VFI models directly exploit existing lightweight network frameworks, thus making synthesized in-between frames blurry and creating artifacts due to imprecise motion representation. The other existing VFI models typically depend on heavy model architectures with a large number of parameters, preventing them from being deployed on small terminals. To address these issues, we propose a local lightweight VFI network (L2BEC2) that leverages bidirectional encoding structure with channel attention cascade. Specifically, we improve visual quality by introducing a forward and backward encoding structure with channel attention cascade to better characterize motion information. Furthermore, we introduce a local lightweight strategy into the state-of-the-art Adaptive Collaboration of Flows (AdaCoF) model to simplify its model parameters. Compared with the original AdaCoF model, the proposed L2BEC2 obtains performance gain at the cost of only one-third of the number of parameters and performs favorably against the state-of-the-art works on public datasets. Our source code is available at https://github.com/Pumpkin123709/LBEC.git.

Deep Neural Networks based video frame interpolation, synthesizing in-between frames given two consecutive neighboring frames, typically depends on heavy model architectures, preventing them from being deployed on small terminals. When directly adopting the lightweight network architecture from these models, the synthesized frames may suffer from poor visual appearance. In this paper, a lightweight-driven video frame interpolation network (L2BEC2) is proposed. Concretely, we first improve the visual appearance by introducing the bidirectional encoding structure with channel attention cascade to better characterize the motion information; then we further adopt the local network lightweight idea into the aforementioned structure to significantly eliminate its redundant parts of the model parameters. As a result, our L2BEC2 performs favorably at the cost of only one third of the parameters compared with the state-of-the-art methods on public datasets. Our source code is available at https://github.com/Pumpkin123709/LBEC.git.

No abstract available

RIFE is a breakthrough in real-time video frame interpolation, introducing the IFNet neural network to estimate intermediate flows directly and efficiently. By avoiding the complexities of bidirectional optical flow estimation, RIFE achieves impressive speed and quality improvements, outperforming leading methods like SuperSlomo and DAIN. This research is timely, addressing the increasing demand for high-quality video content and the need to convert low-frame-rate videos into high-frame-rate content for modern displays. RIFE’s privileged distillation scheme and support for arbitrary-timestep frame interpolation make it a promising solution for real-time video enhancement.

Video frame interpolation presents a formidable challenge in the domain of video generation, primarily due to the intricate motion dynamics exhibited by objects within video frames. With the advancements in deep learning, numerous flow-based methods for video frame interpolation have emerged. These methods aim to predict intermediate frames by leveraging the estimation of motion information between frames. In this paper, we propose a novel framework for modeling input video frames, which employs a coarse-to-fine structure to extract motion information between frames. Additionally, it incorporates a Bidirectional Correlation Volume and a complementary module of contextual features, specifically designed to pay attention to the symmetry of the optical flow and shallow motion features. We incorporate this dual attention to the knowledge distillation part of the model, which further improves the performance of the model. Leveraging this framework, our model demonstrates the ability to accurately predict motion information between frames, consequently producing visually appealing intermediate frames.The code is available at https://github.com/famt0531/DAEK.

No abstract available

Video frame interpolation is an important low-level task in the field of image processing, which is widely applied to video image restoration enhancement, media players and display devices. In this work, we design an optical flow module, termed TFA block, for temporal feature alignment based on spatial-temporal modeling for fast and accurate video frame interpolation. It first matches adjacent input frames into spatial location roughly, then uses spatial-temporal modeling to align spatial features with time domain, and finally merges in time domain dimension to obtain optical flow between input continuous frames and objective frame. TFA block does not need complex network structure or relying on the pre-trained optical flow network, but obtain the task-oriented bidirectional intermediate optical flow from output frame to given inputs for backward warping. Compared to the state-of-the-art (SOTA) algorithms, our network achieves demonstrates both excellent performance improvement and fast inference speed

Video frame interpolation (VFI), which aims to synthesize predictive frames from bidirectional historical references, has made remarkable progress with the development of deep convolutional neural networks (CNNs) over the past years. Existing CNNs generally face challenges in handing large motions due to the locality of convolution operations, resulting in a slow inference structure. We introduce a Real-time video frame interpolation transformer (RVFIT), a novel framework to overcome this limitation. Unlike traditional methods based on CNNs, this paper does not process video frames separately with different network modules in the spatial domain but batches adjacent frames through a single UNet-style structure end-to-end Transformer network architecture. Moreover, this paper creatively sets up two-stage interpolation sampling before and after the end-to-end network to maximize the performance of the traditional CV algorithm. The experimental results show that compared with SOTA TMNet, RVFIT has only 50% of the network size (6.2M vs 12.3M, parameters) while ensuring comparable performance, and the speed is increased by 80% (26.1 fps vs 14.3 fps, frame size is 720*576).

Existing optical flow-based frame interpolation frameworks usually suffer from two problems. First, it is difficult to accurately estimate both large motion and fine motion in the optical flow estimation stage. Second, the hole problem and occlusion problem cannot be efficiently solved in the pixel synthesis step. In this paper, we propose a novel optical flowbased frame interpolation framework, which consists of two submodules: optical flow network and pixel synthesis network. In the optical flow network, we estimate bidirectional optical flow sequences iteratively, which makes full use of the continuity of motion and therefore improves the accuracy of the optical flow estimation. Besides, a novel multi-scale architecture is developed to capture finer motions. In the pixel synthesis network, we fuse the statistical information generated during forward warping to solve the hole problem and the occlusion problem. Experimental results demonstrate that the proposed method achieves superior performance compared to state-of-the-art methods.

No abstract available

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Optical flow estimation is widely used in fields such as video frame interpolation, object tracking, and scene understanding. Although existing deep learning models have significantly improved the accuracy of optical flow estimation, they are often hindered by high model complexity and a lack of effective cyclic consistency constraints for the generated optical flows. To address this issue, this paper proposes a lightweight optical flow estimation model and uses cyclic consistency constraints to improve the quality of both forward and backward optical flow generation. The main contributions of this paper are: proposing a lightweight optical flow estimation model based on U-Net and introducing cyclic consistency constraints to enhance both the accuracy and physical consistency of optical flow generation. Experimental results on the knee joint dataset show that the improved bidirectional optical flow estimation module reduces the number of parameters by approximately 37.47%, while achieving higher PSNR and SSIM than the original module.

Space-time video super-resolution aims to reconstruct the high-frame-rate and high-resolution video from the corresponding low-frame-rate and low-resolution counterpart. Currently, the task faces the challenge of efficiently extracting long-range temporal information from available frames. Meanwhile, existing methods can only produce results for a specific moment and cannot interpolate high-resolution frames for consecutive time stamps. To address these issues, we propose a multi-stage feature enhancement method that better utilizes the limited spatio-temporal information subject to the efficiency constraint. Our approach involves a pre-alignment module that extracts coarse aligned features from the adjacent odd-numbered frames in the first stage. In the second stage, we use a bidirectional recurrent module to refine the aligned features by exploiting the long-range information from all input frames while simultaneously performing video frame interpolation. The proposed video frame interpolation module concatenates temporal information with spatial features to achieve continuous interpolation, which refines the interpolated feature progressively and enhances the spatial information by utilizing the features of different scales. Extensive experiments on various benchmarks demonstrate that the proposed method outperforms state-of-the-art in both quantitative metrics and visual effects.

No abstract available

Video frame interpolation (VFI) is significant for generating a high frame rate coronary sequence without additional radiation exposure. Due to the coronary reciprocating pattern alternating between systolic and diastolic phases, the linear assumption-based existing methods fail to capture the complex motion especially during the transitions between the two phases. Different from the linear methods, a Non-linear Motion Estimation Network (NLME-Net) is proposed to effectively capture the periodic reciprocating motion pattern by accurately estimating both bidirectional flows and long-distance motion. Specifically, the specialized motion estimation decoder is guided not only by target frame reconstruction loss but also by direct supervision through a self-supervised flow loss. This enhanced modeling of reciprocating motion enables accurate intermediate flow estimation in scenarios involving variable directional movement, thereby improving the accuracy and robustness of frame interpolation. Additionally, the interpolation decoder fully exploits the inherent mutual dependency between intermediate flow and target frame features to refine the final interpolation result. According to the experiment results of the proposed and twelve state-of-the-art methods using the coronary dataset with 6486 groups of angiographic images from 399 sequences, the proposed method improves the PSNR score by an average 0.59dB.

Due to the incomplete coverage and failure of traffic data collectors during the collection, traffic data usually suffers from information missing. Achieving accurate imputation is critical to the operation of transportation networks. Existing approaches usually focus on the characteristic analysis of temporal variation and adjacent spatial representation, and the consideration of higher-order spatial correlations and continuous data missing attracts more attentions from the academia and industry. In this paper, by leveraging motif-based graph aggregation, we propose a spatiotemporal imputation approach to address the issue of traffic data missing. First, through motif discovery, the higher-order graph aggregation model was presented in traffic networks. It utilized graph convolution network (GCN) to polymerize the correlated segment attributes of the missing data segments. Then, the multitime dimension imputation model based on bidirectional long short-term memory (Bi-LSTM) incorporated the recent, daily-periodic, and weekly-periodic dependencies of the historical data. Finally, the spatial aggregated values and the temporal fusion values were integrated to obtain the results. We conducted comprehensive experiments based on the real-world dataset and discussed the case of random and continuous data missing by different time intervals, and the results showed that the proposed approach was feasible and accurate.

Although numerous spatiotemporal approaches have been presented to address the problem of missing spatiotemporal data, there are still limitations in concurrently capturing the underlying spatiotemporal dependence of spatiotemporal graph data. Furthermore, most imputation methods miss the hidden dynamic connection associations that exist between graph nodes over time. To address the aforementioned spatiotemporal data imputation challenge, we present an attention-based message passing and dynamic graph convolution network (ADGCN). Specifically, this paper uses attention mechanisms to unify temporal and spatial continuity and aggregate node neighbor information in multiple directions. Furthermore, a dynamic graph convolution module is designed to capture constantly changing spatial correlations in sensors utilizing a new dynamic graph generation method with gating to transmit node information. Extensive imputation tests in the air quality and traffic flow domains were carried out on four real missing data sets. Experiments show that the ADGCN outperforms the state-of-the-art baseline.

No abstract available

Abstract Accurate prediction of traffic status in real time is critical for advanced traffic management and travel navigation guidance. There are many attempts to predict short-term traffic flows using various deep learning algorithms. Most existing prediction models are only tested on spatiotemporal data assuming no missing data entries. However, this ideal situation rarely exists in real world due to sensor or network transmission failure. Missing data is a nonnegligible problem. Previous studies either remove time series with missing entries or impute missing data before building prediction models. The former may cause insufficient data for model training, while the latter adds extra computational burden and the imputation accuracy has direct impacts on the prediction performance. In this study, we propose an online framework that can make spatiotemporal predictions based on raw incomplete data and impute possible missing values at the same time. We design a novel spatial and temporal regularized matrix factorization model, namely LSTM-GL-ReMF, as the key component of the framework. The Long Short-term Memory (LSTM) model is chosen as the temporal regularizer to capture temporal dependency in time series data and the Graph Laplacian (GL) serves as the spatial regularizer to utilize spatial correlations among network sensors to enhance prediction and imputation performance. The proposed framework integrating with the LSTM-GL-ReMF model are tested and compared with other state-of-the-art matrix factorization models and deep learning models on three uni-variate and multi-variate spatiotemporal traffic datasets. The experimental results show our approach has a robust and accurate performance in terms of prediction and imputation accuracy under various data missing scenarios.

The widespread deployment of roadside sensors in cooperative vehicle-infrastructure systems enables large-scale vehicle trajectory data collection, crucial for trajectory planning and driving safety analysis of autonomous vehicles. However, sensor failure and environmental interference often lead to significant data gaps. To address this issue, we propose a Graph Transformer-based Trajectory Imputation (GTTI) model, which utilizes a Scalable Graph Transformer (SGT) to reconstruct missing trajectories by capturing multi-vehicle interactions and integrating spatiotemporal semantics of driving scenarios. Combining attention mechanisms and semantic understanding, the GTTI effectively handles large-scale imputation, even in complex traffic scenarios with substantial data loss. Extensive evaluations using real-world highway data were carried out. The results show that GTTI outperforms state-of-the-art models, improving imputation accuracy by 12.7% in Average Displacement Error (ADE) and 8.8% in Final Displacement Error (FDE).

No abstract available

During traffic data acquisition, missing data often arise owing to equipment failures and network disruptions. Despite extensive research on traffic data imputation, two primary limitations persist: First, existing methods struggle to fully integrate the spatiotemporal correlations and low-rank structures inherent in traffic data. Second, current research has mostly focused on missing completely at random (MCAR), with limited attention on other missing data patterns. We propose an innovative method, tensor completion and graph network fusion (TCGNF), to address these challenges for missing traffic data imputation. This method initially utilizes tensor completion for the preliminary imputation of missing data. Subsequently, it constructs the road network by leveraging the Pearson correlation coefficient from historical road data and the physical distances between detectors. The method then uses graph sampling and aggregation (GraphSAGE) to extract spatiotemporal data features from the two road networks and fuse them. Finally, these features are trained in generative adversarial networks (GANs) for accurate data imputation. Extensive experiments were conducted on two publicly accessible traffic datasets to validate the efficacy of the TCGNF model. The outcomes of these experiments indicate that the TCGNF model demonstrates superior generalization capabilities, significantly outperforming other state-of-the-art data imputation models concerning overall performance.

Missing sensor data in cultural heritage monitoring (e.g., microclimate monitoring) compromises time series continuity and threatens the assessment of critical indicators such as rock stability. Existing imputation methods often ignore spatial correlations in sensor networks and underperform in modeling nonstationary periodic patterns. To address this, we propose TPE-GRIN, a novel framework integrating Temporal Positional Encoding (TPE) with a Graph Recurrent Imputation Network (GRIN). The TPE module generates position-aware features via sine/cosine functions to adaptively fuse spatiotemporal signals for capturing diurnal/seasonal fluctuations, while the bidirectional GRIN architecture jointly models sensor topology dependencies and historical-future trends through Message-Passing Gated Units. When evaluated on the Yungang Grottoes dataset, TPE-GRIN outperforms the best baseline model GRIN in both prediction accuracy and handling long-block missing data scenarios, providing high-integrity data support for optimizing downstream sensor deployment.

Missing data is ubiquitous phenomenon in the time series community, significantly challenging forecasting due to incomplete ground truth and sparse data. Most previous Multi-variate Time Series Forecasting with Missing Values (MTSFMV) approaches usually assume static missing patterns, neglecting the dynamic changes over time and space, leading to suboptimal forecasting results. To tackle these challenges, we propose novel STMPANets, which are capable of perceiving time-varying spatiotemporal missing patterns to refine the forecasting sequences. Specifically, we decompose the series into seasonal trend components, allowing STMPANets to highlight inherent sequence properties and adapt to missing patterns. We then propose a Multi-granularity Conditional Partial TCN (MGCPT) to regulate the imputation rate of missing values over time, modeling temporal correlation. Additionally, we design an Adaptive Dynamic GCN (ADGCN) to capture spatial dependencies by perceiving dynamic missing patterns. Extensive experiments demonstrate that STMPANets outperform state-of-the-art models.

Monitoring Chlorophyll-a (Chl-a) concentration in ocean is of considerable significance for early warning of algae disasters, marine ecological environment protection, etc. However, due to various uncontrollable factors such as cloud cover and thick aerosols, the missing rate of observed Chl-a data is quite high, which seriously hinders its applications. The existing data imputation methods are mostly applicable to Chl-a data with a low missing rate, and perform much worse when the missing rate reaches 0.7 or above. To address this issue, we proposed a self-supervised spatiotemporal imputation (S2-STI) model for highly sparse Chl-a data imputation by fusing multisource satellite data. First, to obtain comprehensive information about the missed Chl-a data, we designed a multisource sparse data fusion (MSDF) module to fuse multisource satellite data, including Chl-a data, sea surface temperature (SST) data, and photosynthetically available radiation data. MSDF constructs a spatialtemporal graph network to learn high-quality spatiotemporal representations of SST and photosynthetically active radiation (PAR) data, and fuses the learned representations with Chl-a data to enrich the information for imputation. Then, we developed a generation-based data imputation (GDI) module to model the distribution of Chl-a data based on the outputs of MSDF. Considering the high data sparsity, we designed a self-supervised training strategy to train S2-STI in the absence of ground truth. Finally, we leverage the data generated by the GDI module in the trained S2-STI model to fill in missing values in the sparse Chl-a data. Experiments on real datasets show that S2-STI achieves much better performance than the existing data imputation methods. Specifically, for the Chl-a data with a missing rate of 0.9, S2-STI improves by at least 12% in terms of masked autoencoder (MAE) error when compared with the strong baseline methods.

Traffic data imputation is crucial for the reliability and efficiency of intelligent transportation systems (ITSs), forming the foundation for downstream tasks like traffic prediction and management. However, existing deep learning-based imputation methods struggle with two significant challenges: poor performance under high missing data rates and the limited incorporation of external traffic-related factors. To address these challenges, we propose a novel knowledge graph-enhanced generative adversarial network (KG-GAN) for traffic data imputation. Our approach uniquely integrates external knowledge with traffic spatiotemporal dependencies to improve data imputation quality. Specifically, we construct a fine-grained knowledge graph (KG) that differentiates attributes and relationships of external factors such as points of interest (POI) and weather conditions, facilitating more robust knowledge representation learning. We then introduce a knowledge-aware embedding cell (EM-cell) that merges traffic data with these learned external representations, providing richer inputs for the spatiotemporal GAN. Extensive experiments on a large-scale real-world traffic dataset demonstrate that KG-GAN significantly outperforms state-of-the-art methods under various missing data scenarios. Additionally, ablation studies confirm the superior performance gained from incorporating external knowledge, underscoring the importance of this approach in addressing complex missing data patterns.

When dealing with time series data, handling missing values has always been an unavoidable challenge. Effective time series imputation methods allow for the reconstruction of missing time data by leveraging information from different sensors. However, current methods often fail to fully exploit the spatial relationships between different sensors and overlook the continuity of time series. In this work, we evaluate graph neural networks in the context of multivariate time series imputation. Therefore, we introduce a novel graph neural network architecture called MGGNet, aimed at learning spatiotemporal representations to reconstruct entire multivariate time series for imputation purposes. Empirical results demonstrate that our model outperforms state-of-the-art methods in imputation tasks on relevant real-world benchmarks.

Accurate imputation of missing data in air quality monitoring is essential for reliable environmental assessment and modeling. This study compares two imputation methods, namely Random Forest (RF) and Bidirectional Recurrent Imputation for Time Series (BRITS), using data from the Mexico City air quality monitoring network (2014–2023). The analysis focuses on stations with less than 30% missingness and includes both pollutant (CO, NO, NO2, NOx, SO2, O3, PM10, PM2.5, and PMCO) and meteorological (relative humidity, temperature, wind direction and speed) variables. Each station’s data was split into 80% for training and 20% for validation, with 20% artificial missingness. Performance was assessed through two perspectives: local accuracy (MAE and RMSE) on masked subsets and distributional similarity on complete datasets (Two One-Sided Tests and Wasserstein distance). RF achieved lower errors on masked subsets, whereas BRITS better preserved the complete distribution. Both methods struggled with highly variable features. On complete time series, BRITS produced more realistic imputations, while RF often generated extreme outliers. These findings demonstrate the advantages of deep learning for handling complex temporal dependencies and highlight the need for robust strategies for stations with extensive gaps. Enhancing the accuracy of imputations is crucial for improving forecasting, trend analysis, and public health decision-making.

For the real-world time series analysis, data missing is a ubiquitously existing problem due to anomalies during data collecting and storage. If not treated properly, this problem will seriously hinder the classification, regression, or related tasks. Existing methods for time series imputation either impose too strong assumptions on the distribution of missing data or cannot fully exploit, even simply ignore, the informative temporal dependencies and feature correlations across different time steps. In this article, inspired by the idea of conditional generative adversarial networks, we propose a generative adversarial learning framework for time series imputation under the condition of observed data (as well as the labels, if possible). In our model, we employ a modified bidirectional RNN structure as the generator G, which is aimed at generating the missing values by taking advantage of the temporal and nontemporal information extracted from the observed time series. The discriminator D is designed to distinguish whether each value in a time series is generated or not so that it can help the generator to make an adjustment toward a more authentic imputation result. For an empirical verification of our model, we conduct imputation and classification experiments on several real-world time series data sets. The experimental results show an eminent improvement compared with state-of-the-art baseline models.

No abstract available

Clinical multivariate time series can be used to predict clinical outcomes and in turn support clinical decision. Due to various reasons such as irregular sampling, clinical time series typically contain many missing values, and some missing values contain a large amount of information for clinical prediction. It is important to impute missing values as accurately as possible prior to clinical prediction. However, the missing rate of different variables in clinical time series varies greatly. In addition, clinical time data also has strong burst, which increases the difficulty of missing value imputation. In this paper, we propose a new method for missing value imputation in multivariate time series data, using a trainable weighted decay mechanism to improve the traditional Bi-LSTM model to capture temporal correlations, impute missing values based on bidirectional recurrent neural network and perform clinical outcomes predict. We take the missing rate, cumulative missing rate and burstiness of each variable as input to learn the features of different variables separately and improve the imputation effect of missing values. Experiments on two real-world clinical datasets show that our model achieves optimal performance in both imputation effect and prediction accuracy.

No abstract available

Imputing missing values in high-dimensional time-series data remains a significant challenge in statistics and machine learning. Although various methods have been proposed in recent years, many struggle with limitations and reduced accuracy, particularly when the missing rate is high. In this work, we present a novel f-divergence-based bidirectional generative adversarial imputation network, tf-BiGAIN, designed to address these challenges in time-series data imputation. Unlike traditional imputation methods, tf-BiGAIN employs a generative model to synthesize missing values without relying on distributional assumptions. The imputation process is achieved by training two neural networks, implemented using bidirectional modified gated recurrent units, with f-divergence serving as the objective function to guide optimization. Compared to existing deep learning-based methods, tf-BiGAIN introduces two key innovations. First, the use of f-divergence provides a flexible and adaptable framework for optimizing the model across diverse imputation tasks, enhancing its versatility. Second, the use of bidirectional gated recurrent units allows the model to leverage both forward and backward temporal information. This bidirectional approach enables the model to effectively capture dependencies from both past and future observations, enhancing its imputation accuracy and robustness. We applied tf-BiGAIN to analyze two real-world time-series datasets, demonstrating its superior performance in imputing missing values and outperforming existing methods in terms of accuracy and robustness.

Technological advances in industry have made it possible to install many connected sensors, generating a great amount of observations at high rate. The advent of Industry 4.0 requires analysis capabilities of heterogeneous data in form of related multivariate time series. However, missing data can degrade processing and lead to bias and misunderstandings or even wrong decision-making. In this paper, a recurrent neural network-based denoising autoencoder is proposed for gap imputation in related multivariate time series, i.e., series that exhibit spatio-temporal correlations. The denoising autoencoder (DAE) is able to reproduce input missing data by learning to remove intentionally added gaps, while the recurrent neural network (RNN) captures temporal patterns and relationships among variables. For that reason, different unidirectional (simple RNN, GRU, LSTM) and bidirectional (BiSRNN, BiGRU, BiLSTM) architectures are compared with each other and to state-of-the-art methods using three different datasets in the experiments. The implementation with BiGRU layers outperforms the others, effectively filling gaps with a low reconstruction error. The use of this approach is appropriate for complex scenarios where several variables contain long gaps. However, extreme scenarios with very short gaps in one variable or no available data should be avoided.

Handling missing data is a major challenge in machine learning, particularly in clinical settings using electronic health records like ICU time-series data. Advanced imputation techniques, such as Bidirectional Recurrent Imputation for Time Series (BRITS), Self-Attention-based Imputation for Time Series (SAITS), and Multi-directional Recurrent Neural Network (M-RNN), show strong performance but are influenced by dataset characteristics like missing patterns and feature distributions. This study compares ten imputation methods on the public MIMIC-III database and COPRA, a local hospital dataset. We evaluate classical approaches (Zero, Mean, Median, Last), advanced models (BRITS, SAITS, M-RNN), and their transfer learning (TL) adaptations (TranBRITS, TranSAITS, TranM-RNN). TL was implemented by transforming COPRA to align with MIMIC-III, enabling fine-tuning of pre-trained models. TranSAITS achieved the best performance on the transformed dataset (M->C). Notably, the simple Last method also performed competitively for vital signs, underscoring its potential for real-time clinical use where low complexity and efficiency are key.

Time series clustering is a complex unsupervised data mining and analysis technique that can be applied to various fields such as signal processing, financial analysis, and more. However, time series data often contain missing values due to reasons such as sensor failures, data corruption, or intentional omissions in the real world. Traditional generative imputation methods operate independently from subsequent clustering tasks, and their performance relies on the combination with the clustering method, lacking a deeper connection. Efficiently integrating imputation and clustering tasks into a unified framework remains a formidable challenge. This paper presents a novel model that harmonizes the imputation and clustering processes, referred to as the Conditional Dual-Discriminator Generative Adversarial Network for Incomplete Time Series Data Imputation and Clustering (TsCDD-GAN). The TsCDD-GAN model leverages advanced bi-directional Recurrent Units (Bidirectional RNN) as the generator to learn and impute missing data, integrating two discriminators. The first discriminator assists the generator in producing more authentic values, while the second, a conditional discriminator, extracts clustering information from the latent representations of the data. This enables the generator to not only generate more realistic values but also ensure that the imputed data exhibit cluster-friendly characteristics. Through experiments conducted on the UCR time series dataset, our model has demonstrated better performance in terms of imputation accuracy on incomplete datasets.

Multivariate time-series data are abundant in many application areas, such as finance, transportation, environment, and healthcare. However, for many reasons, missing data points is a common problem, mainly associated with data collected from wearable devices. Missing values negatively impact the performance of data analysis and machine learning algorithms. Various statistical and machine-learning methods have been developed to overcome this challenge, primarily by imputation, i.e., filling in the missing values in the data. In this study, we compare some widely used classical imputation methods such as mean, median imputation, Last Observed Carried Forward (LOCF), K-Nearest Neighbors imputation (KNNI), and some recently developed techniques for time series imputation such as Bidirectional Recurrent Imputation for Time Series (BRITS), Transformer, and Self-attention-based imputation for time series (SAITS). We evaluate these methods on the Crowd-sourced Fitbit dataset on collected activity data through wearables. The results suggest that even though being a classical imputation method, KNNI can be more efficient than some state-of-the-art methods when the missing rate is low to moderate (less than 30%). Meanwhile, at a higher missing rate (greater than or equal to 30%), SAITS is the one that can give the lowest mean absolute error (MAE) with a reasonable execution time.

In industrial monitoring of semiconductor probe cards, real-time sensor data acquisition and processing are essential for anomaly detection and predictive maintenance. However, missing data resulting from possible sensor malfunctions present a significant challenge, compromising the integrity of subsequent analyses. The present study addresses this issue by applying and evaluating a state-of-the-art deep learning approach, the Self-Attention-based Imputation for Time Series model, to reconstruct corrupted signals from an industrial sensor network comprising accelerometers and microphones. A rigorous evaluation was conducted against traditional imputation methods and a powerful deep learning comparison method, the Bidirectional Recurrent Imputation for Time Series model, using a comprehensive set of time- and frequency-domain metrics. The results demonstrate that the self-attention model achieves competitive or superior accuracy, with an average improvement of 66% (with values ranging between 25% and 88%) in Mean Absolute Error over traditional methods especially in scenarios with extensive data loss, ensuring high fidelity in the reconstructed signals. The proposed analysis shows that the attention-based architecture offers a substantial practical advantage, completing training per epoch more than twenty times faster than the recurrent-based comparison method. This balance of high performance and computational efficiency makes the self-attention framework a robust and pragmatic solution to achieve data integrity in demanding monitoring and management systems.

To solve the problems of generative adversarial network (GAN)-based imputation method for time series, which are ignoring the implied trends in data and using multi-stage training that may lead to high training complexity, this article proposes a trend-aware data imputation method based on GAN (TrendGAN). It implements an end-to-end training using de-noising auto-encoder (DAE). It also uses bidirectional gated recurrent unit (Bi-GRU) in the generator model to consider the bi-directional characteristics and supplement the features lost by de-noising auto-encoder and improves the discriminator's ability using Bi-GRU and hint vector. The authors conducted experiments on four real datasets. The results showed that all components introduced into the method contribute to enhancing the imputation accuracy, and the MSE values of TrendGAN are much lower than those of baseline methods when dealing with time series with random and continuous missing patterns. That is, TrendGAN is suitable for data imputation in complex scenarios with two missing patterns coexist, such as electric power and transportation.

This paper presents a novel method for imputing missing data of multivariate time series by adapting the Long Short Term-Memory(LSTM) and Denoising Autoencoder(DAE). Missing data are ubiquitous in many domains; proper imputation methods can improve performance on many tasks. Our method focus on multivariate time series, applying bidirectional LSTM to learn temporal information and DAE to learn correlation between variables, and we combine these two models by using LSTM as the encoder component of DAE. Several real-world datasets, including electroencephalogram(EEG), electromyogram(EMG) and electronic health records(EHRs), are extracted to test the performance of our method. Through simulation studies, we compare the proposed recurrent denoising autoencoder with several baseline imputation methods and demonstrate its effectiveness in both missing data estimation and label prediction after imputation.

In multivariate time series (MTS), missing data will lead to inaccurate predictions. In this paper, we propose a multivariate time series forecasting model based on bidirectional gated recurrent neural networks (RNN) combining self-attention with residual connections, abbreviated as BGRRSA. At the same time, the model also uses univariate time series prediction to extract historical information from the target series. Finally, the outputs of the multi-level self-attention mechanism and univariate time series prediction are weighted and summed to obtain the model's final prediction. Experiments were conducted to compare and analyze different missing values imputation methods and different time series prediction methods on two datasets, verifying the effectiveness and accuracy of the model.

ABSTRACT Due to sensor failures and extreme weather conditions, missing wind speed observations frequently occur, which undermines the accuracy of wind resource assessment and underscores the necessity for accurate data imputation. This study conducts a systematic comparison of different neural network models for wind speed imputation, contrasting two classical models, adaptive backpropagation and long short-term memory with seven emerging multivariate time series neural network models, i.e. Transformer, bidirectional recurrent imputation for time series (BRITS), spectral temporal graph neural network for time series (StemGNN), patch time series Transformer (PatchTST), temporal 2D-variation modeling for time series (TimesNet), frequency-domain MLPs in time series (FreTS) and self-attention-based imputation for time series (SAITS), which have not previously been applied in wind speed data imputation. Using meteorological tower data, the models were evaluated across three distinct terrains, i.e. plain, mountain, and plateau, under diverse missing patterns and ratios. Results showed that the SAITS model consistently outperformed all others, particularly in the complex plateau terrain with high missing rates, followed closely by Transformer and PatchTST. These advanced models, leveraging self-attention and sophisticated sequence modeling, excelled in capturing nonlinear temporal dependencies, far surpassing the limited performance of BP and LSTM in challenging conditions. The SAITS model achieved error reductions of up to 46.1% in root mean squared error compared to the classical neural network models in complex plateau terrain at 50% missing ratio, followed closely by Transformer and PatchTST, which reduced errors by approximately 44.5% and 36.6%, respectively. This study highlights the potential of self-attention-based neural architectures for enhancing wind speed imputation accuracy, enabling more precise wind resource assessment.

ABSTRACT Reconstructing high-quality Normalized Difference Vegetation Index time series data is essential for ecological and agricultural applications but remains challenging in heavily cloudy areas. Fusing Sentinel SAR and optical data with deep learning could be helpful but is also challenging for stable models due to unstable SAR-NDVI relationships caused by imaging mechanism differences and environmental complexities. In this study, we developed a new Bidirectional Recurrent Imputation for Optical-SAR fusion (BRIOS) model to reconstruct high-quality Sentinel-2 NDVI time series data. BRIOS designs a two-layer recurrent architecture that integrates the autocorrelation of discrete, cloud-free NDVI observations into the model for a more stable SAR-NDVI relationship. Evaluating BRIOS against three baseline methods (GF-SG spatiotemporal fusion, Harmonic regression interpolation, and MCNN-Seq deep learning) across three full Sentinel-2 tiles in reconstructing 8-day NDVI time series, BRIOS consistently outperformed in scenarios of either random or continuously missing data, as evidenced by lower RMSE values (e.g. 0.075 for BRIOS vs. 0.108 for GF-SG vs. 0.143 for Harmonic regression vs. 0.303 for MCNN-Seq), better Edge index, and high linear correlation coefficients (R values up to 0.97). Further ablation experiments revealed that deep integration of NDVI autocorrelation features and SAR temporal change patterns has improved the stability and generalization of BRIOS. Discussions on the model's scalability across various cloud sizes and training dataset sizes affirm its practicality for broad-scale application in vegetation monitoring under challenging cloudy conditions.

Characterization of turbulent flows is challenging due to the interaction of widespread spatiotemporal scales. Experimental techniques such as Particle Image Velocimetry (PIV) can be used to obtain spatially resolved flow measurements, however, these systems often suffer from limited acquisition rates. The present work investigates the ability of an advection-based flow reconstruction technique to increase the temporal resolution of turbulent flow data without any prior knowledge of the flow physics. A semi-Lagrangian technique is suggested to obtain fluid trajectories through a forward and backward integration of the available spatiotemporal data. The estimates are then fused using a temporal weighting scheme to yield velocity fields at intermediate times. The performance of the method is verified against three-dimensional direct numerical simulation (DNS) data of a plane jet at Re = 10000. Extracting time series data from the spatially and temporally resolved DNS results, five test cases with artificially lowered sampling frequencies were generated. Spectral analysis revealed that the characteristic frequency found in shear-layer dominated flows can be obtained even for the most extreme case. Additionally, spectral information up to two orders of magnitude beyond the Nyquist criteria is successfully recovered throughout the entire spatial domain -- surpassing the performance of previously introduced methods. The maximum spectral reconstruction error of the suggested method, defined as net energy loss or gain, fell within the bounds of [-5, 3]%, with a corresponding global energy difference in the range of [-2, 1]%. Furthermore, the spatially averaged reconstruction error for the velocity fluctuations was bound by [6 +/- 6]%.

The present work investigates the performance of an advection-based flow reconstruction model to increase the temporal resolution of PIV measurements recorded in a turbulent, planar jet. Using a semi-Lagrangian technique in combination with Rapid Distortion Theory, a modified trajectory tracking procedure is implemented. The method introduces a specification for a two-dimensional convective velocity based on the least squares minimization of the linearized advection equation, in contrast to the previously introduced one-dimensional mean velocity profile outlined in Vocke et al. (2023). The new implementation is based on local flow measurements, making it well-suited towards streamwise heterogeneity and spatially developing flows. With this, the flow at some unknown time can be estimated from the know flow measurements at the forward and backward time. Spectral analysis illustrates the model's proficiency in recovering spatiotemporal information far exceeding the Nyquist frequency, with spectral reconstruction errors of less than 5% for the most extreme case. It is demonstrated that the spectral content can be estimated at least two orders of magnitude beyond the sampling frequency of the original recording. Improved performance compared to alternative methods is demonstrated with only minor impact on computational time. This indicates the approach may be used as a tool for experimental researchers a) having no access to a high-speed PIV or b) with high-speed PIV to increase the spectral resolution even further.

In this article we introduce a novel method for improving the accuracy of density reconstructions based on markers pushed forward by some available particle code. The method relies on the backward Lagrangian representation of the transported density, and it evaluates the backward flow using the current position of point particles seen as flow markers. Compared to existing smooth particle methods with either fixed or transformed shapes, the proposed reconstruction achieves higher locality and accuracy. This is confirmed by our error analysis which shows a theoretical gain of one convergence order compared to the LTP/QTP methods introduced in [Campos Pinto, M., 2015. Towards smooth particle methods without smoothing. Journal of Scientific Computing, 65, pp.54–82], and by numerical experiments that demonstrate significative CPU gains and an improved robustness relative to the remapping period.

In this study, we examined salinity fields as both passive and active tracers to generate high-resolution sea surface salinity fields using a Lagrangian reconstruction technique, integrating satellite-derived data and numerical advection schemes. Specifically, we employed Version 4.0 of NASA’s Soil Moisture Active Passive (SMAP) Level-3 sea surface salinity product, which features an 8-day running mean and approximately 25 km spatial resolution. Geostrophic surface currents at comparable spatial resolution, sourced from satellite altimetry data provided by the Copernicus Marine Environment Monitoring Service (CMEMS), were utilized in this work. By applying backward and forward numerical advection schemes to the SMAP sea surface salinity fields using these altimetry-derived currents, we captured smaller-scale salinity features, generating reconstructed fields on a 4-km output grid. The passive-advection implementation was first verified in the Gulf Stream through comparison with the published reconstruction of Barceló-Llull et al. (2021), after which the framework was applied and further developed for the Bay of Bengal, the primary study region. Utilizing salinity as a passive tracer allowed us to focus exclusively on horizontal advection without accounting for sources, sinks, or mixing. A sensitivity analysis was performed, which determined that the highest feasible resolution using this approach is 4 km, with an optimal advection integration period of 14 days. Preliminary validation against ship-based thermo-salinograph observations from 2015 to 2024 demonstrates that High-Resolution Sea Surface Salinity via Passive Advection (HRSSS-PA) achieves RMSEs of 0.19 to 3.19 PSU with correlations of 0.12 to 0.93, generally outperforming SMAP, which shows higher errors (0.21 to 4.78 PSU) and weaker or inconsistent correlations (-0.19 to 0.96). This highlights the ability of HRSSS-PA to capture both magnitude and fine-scale salinity variability. To address cases where the assumptions of passive advection break down, the framework was further extended to an active advection approach, in which salinity values were dynamically adjusted during transport to account for freshwater input and precipitation, enabling improved representation under conditions characterized by strong freshwater forcing, sharp sea-surface salinity gradients, and river-plume influence.

The calculation of the weight matrix is one of the key steps of the tomographic reconstruction in the light field particle image velocimetry (light field PIV) system. At present, the existing calculation method of the weight matrix in light field PIV based on the forward ray-tracing technique (named Fahringer’s method) is very time-consuming. To improve the computational efficiency of the weight matrix, this paper presents a computational method for the weight matrix based on the backward ray-tracing technique in combination with a Gaussian function (named the Gaussian function method). An expectation–maximization algorithm is employed for the reconstruction of the 3D particle field, and a summed line-of-sight (SLOS) estimation is further used to accelerate the reconstruction process. The computational accuracy and efficiency of the weight matrix, the reconstruction quality of the 3D particle field, and the velocity field accuracy by the Gaussian function method are numerically investigated. Finally, experiments are carried out to verify the feasibility of the weight matrix by the Gaussian function method. The numerical results illustrated that the Gaussian function method can improve the computational efficiency of the weight matrix more than ten times. The SLOS is capable of further accelerating the computational efficiency of the overall reconstruction process, including the pre-determination, the calculation of the weight matrix and the reconstruction. The velocity field accuracy by the Gaussian function method is almost the same as that by Fahringer’s method. The experimental results of the three-dimensional and three-component velocity field of a laminar flow further verify the feasibility of the computational method for the weight matrix based on the Gaussian function method.

No abstract available

One of the reasons for the limited applicability of predictive water quality models is the lack of data from monitoring control stations that are required as input. In this context, the main novelty of the present work is the recovery of information on the state variables present in a water quality model through measured data at a target downstream location. The reconstruction of the upstream boundary condition is the goal of the present work. For this purpose, an adjoint-state method is developed to find the sensitivities of the functional with respect to variations on the upstream boundary conditions of the model. The resolution of both forward and backward problems ensures strong, accurate and reliable solutions in both steady state and unsteady scenarios. The different cases demonstrate that the method is able to reconstruct any observed distribution with little computational effort, including the heat balance with all its external inputs.

No abstract available

OBJECTIVE This work aims to investigate the benefits of incorporating fluid dynamic models into ultrasound vector flow imaging through a novel data assimilation framework using tensor product B-splines for model-based regularization. METHODS A variational data assimilation method was developed using tensor product B-splines with the goal of solving high-dimensional regularization problems governed by the Navier-Stokes equations. The method was implemented in an open-source library and validated across three experimental setups: in silico using a computational fluid dynamics phantom, in vitro using a pulsatile flow phantom with particle imaging velocimetry and in vivo using 4-D ultrasound compared with magnetic resonance imaging. RESULTS The proposed method outperformed conventional smoothing techniques and matched the performance of state-of-the-art regularization approaches. In silico tests showed improved noise suppression and lower root mean squared error. In vitro experiments demonstrated accurate reconstruction of flow features and gradient-based metrics. In vivo comparisons revealed good agreement with magnetic resonance imaging in high-velocity regions and successful reconstruction in dropout zones. CONCLUSION The data assimilation approach using B-splines and fluid dynamic constraints enables efficient and accurate reconstruction of 4-D flow fields in ultrasound vector flow imaging. It offers a promising solution for bedside clinical applications, balancing noise suppression and resolution while leveraging physical models for robust flow estimation.

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Abstract Reynolds-averaged Navier–Stokes (RANS)-based data assimilation has proven to be essential in many data-driven approaches, including the augmentation of experimental data and the identification of turbulence model corrections. As dense measurements of the whole mean flow are not always available when performing data assimilation, we here investigate the case where only a few punctual mean velocity measurements are employed to infer the full mean flow. Sensor placement methodologies are developed targeting an enhancement in either (i) the extrapolation of the full mean velocity field from the few punctual measurements or (ii) the identification of the considered model correction, which is here a forcing term in the momentum equations that accounts for the divergence of the Reynolds stress tensor. Concerning the first objective, a sensor placement procedure based on the correct reconstruction of the dominant singular modes of the linearized RANS equations is developed. When focusing on retrieving the model correction, we propose in particular a second-order adjoint-based approach to improve the well posedness of the data assimilation problem. It consists in minimizing the condition number of the Hessian operator that is associated with the cost function to optimize in data assimilation. This procedure allows us to take into account all nonlinearities in the present inverse problem during the optimization of the sensor locations, thus ensuring its effectiveness. Numerical experiments on the reconstruction of the mean flow around a circular cylinder at $Re=150$ confirm the validity of the developed sensor placement methodologies, which enable a significant improvement in the fidelity of the reconstructed flow with respect to the true one in multiple scenarios in terms of number of sensors and initial network arrangements.

No abstract available

A methodology is presented that exploits both data-assimilation techniques and resolvent analysis for reconstructing turbulent flows, containing organized structures, with an efficient set of measu...

Accurate prediction of flow field in centrifugal compressors using the present turbulence model remains challenging due to intense nonlinearity and strong adverse pressure gradients inherent in the flow. An ensemble-Kalman-filter-based data assimilation (DA) framework is developed to optimize the RNG (renormalization group) k–ε turbulence models for enhancing prediction accuracy. The DA-optimized RNG k–ε model eliminates anomalous static pressure peaks within high-pressure gradient regions, leading to a more physical pressure distribution. Compared with the original results, the maximum absolute percentage error of static pressure is reduced from 19.98% to 7.24%, and the mean absolute percentage error from 5.12% to 2.77%, achieving a significant improvement in prediction accuracy. Furthermore, constrained by compressor geometry and experimental costs, reconstruction from sparse measurements is critically needed. A sparse-sensing shallow neural network (SS-SNN) is therefore proposed to reconstruct the static pressure field using limited sensing data. The SS-SNN results achieve the maximum absolute percentage error of 7.80% and the mean absolute percentage error of 2.18%. These results indicate that DA-corrected turbulence model and SS-SNN reconstruction offer can rapidly and accurately determine the static pressure distribution in centrifugal compressors.

Reconstructing hidden thermal and flow structures from limited observations is a fundamental challenge in many scientific disciplines. Particles passively advected by the surrounding fluid often encode valuable information along their trajectories, but such data are typically sparse and noisy. To infer the comprehensive dynamics of thermally driven flows from such limited information, we develop a four-dimensional variational (4DVar) Marker-in-Cell method. Its application to laboratory data demonstrates successful reconstruction of the time-dependent temperature field and the Rayleigh number—unobservable yet essential for understanding thermal forcing and heat transport—by assimilating particle trajectories with the governing equations. Furthermore, our method enables prediction of future evolution beyond the assimilation window, yielding results that are consistent with actual observations. We critically assess the method’s performance in light of convective dynamics, identifying the conditions under which it is effective and outlining directions for future refinement. These findings highlight the utility of 4DVar not only for retrospective reconstruction but also for forward prediction of convective behavior, offering a robust framework for analyzing thermally or compositionally driven flows in geophysical and engineering systems.

No abstract available

No abstract available

Daily reservoir water level reconstruction remains challenging when satellite observations are sparse and temporally irregular. This study proposes a framework integrating multisource remote sensing, gated recurrent unit (GRU) priors, and ensemble Kalman filtering/smoothing (EnKF/EnKS), using the Fengtan Reservoir as a case study. Water surface areas derived from Landsat, Sentinel-1, and Sentinel-2 were fused and converted to satellite-derived water levels using an area–water level relationship established from ICESat-2 altimetry. Meteorological forcing variables and accumulated indices were used to generate GRU priors, while EnKF/EnKS assimilated satellite-derived water levels into the GRU priors to reconstruct daily water levels from 2000 to 2024. The results showed that validation based on 312 same-day matched observations yielded an R2 of 0.87 and a root-mean-square error (RMSE) of 3.23 m. During 2000–2014, the GRU prior achieved an RMSE of 5.51 m, an R2 of 0.53, and a Kling–Gupta efficiency (KGE) of 0.63. EnKS reduced the RMSE to 4.92 m and increased R2 and KGE to 0.68 and 0.82, respectively. EnKF/EnKS constrained GRU priors using sparse satellite observations, reducing error accumulation and trajectory drift during long-term inference. The framework provides a feasible approach for long-term water level reconstruction under sparse and irregular satellite observations.

To improve the predictive accuracy of numerical simulations for ventilated cavitating flows, this study presents a data assimilation framework based on the Ensemble Kalman Filter (EnKF) to calibrate four key parameters in a large eddy simulation model for an axisymmetric body: the Smagorinsky constant, the number of smoothing iterations for interface curvature calculation, the characteristic velocity, and the characteristic length. Thirty parameter sets generated via Latin hypercube sampling are utilized to establish the initial flow field ensemble. Using time-series cavity lengths from water tunnel high-speed photography as observational data, an iterative EnKF algorithm derives the optimal parameter combination (CS = 0.0773, MM = 4, U = 0.7873U0, and L = 3.646D). Results demonstrate that the optimized model reduces the relative error of time-averaged cavity length from 7.8% (baseline) to 1.37% against experimental data. Furthermore, while activating subgrid dissipation and interfacial smoothing successfully filters out unphysical grid-scale numerical currents and regularizes macroscopic phase-boundary stability, the single-scalar length observation primarily constrains global geometric scales, leaving fine-scale transient shedding frequencies and localized gas leakage dynamics loosely constrained. Cross-condition validations across varying ventilation rates and freestream velocities confirm the strong multi-condition generalizability of the calibrated parameter matrix for macroscopic cavity predictions.

Ensuring the operational safety of urban air mobility (UAM) in high-density environments relies on real-time, high-resolution sensing of the low-altitude wind field. Traditional computational fluid dynamics is constrained by the trade-off between computational efficiency and transient accuracy, while sparse sensor observations fail to capture full three-dimensional spatial flow fields. This study introduces a reduced-order data assimilation framework that integrates scale-adaptive simulation with a three-dimensional variational algorithm accelerated via proper orthogonal decomposition subspaces. Real-time, sparse LiDAR observations are dynamically mapped into a low-dimensional physical subspace, preserving macroscopic transport constraints while eliminating iterative loops. The framework is validated against the urban canopy flow around the Shenzhen Electronics Group Plaza. Statistical cross-validation suggests that the framework rectifies numerical background biases, reducing the root mean square error of three-dimensional velocity components by 77.8%–86.9% within the observation envelope. Furthermore, local spatial generalization analysis indicates that the framework replicates high-altitude turbulence intensity profiles across downstream blind zones, while restricting an online solution latency to 0.0414 ms per step. This framework provides a low-latency, physically constrained foundation for online UAM trajectory planning and risk forecasting.

Data assimilation practitioners must make design decisions regarding the influence of uncertainties across space, time, and interdependent channels. Using the local ensemble transform Kalman filter, we investigate how different information sharing strategies, namely, strong and weak coupling, affect our ability to reconstruct electrical activity in the heart from sparse observations of state. These two coupling approaches differ in whether observations of one variable are allowed to influence others during the update step. We analyze the potential of a single observation to affect the ensemble weights and span through the spectral properties of the analysis operators. We apply weak and strong coupling in assimilations of observations generated from a numerical model of scroll-wave turbulence and find that restricting information flow from the observations across variable fields (weak coupling) in the low-model error case is effective at improving reconstruction accuracy and robustness. Weak coupling is relatively detrimental for high-model-error reconstructions, and strong coupling produces more reliable estimates of the state. We also consider a case where observations are derived from paced cardiac tissue where only surface voltage is recorded and find in that scenario that while both coupling methods achieve similar degrees of accuracy, strong coupling more closely approximates fine details in the observations, whereas weak coupling provides greater robustness. We conclude that coupling has marginal influence on reconstruction accuracy for cardiac electrical excitation except in extreme cases, i.e., where high-model error precludes accurate reconstruction.

Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet approximating the complete spatio-temporal trajectory is essential for mechanistic insight and understanding, model calibration, and operational decision-making. We introduce LAPIS-SHRED (LAtent Phase Inference from Short time sequence using SHallow REcurrent Decoders), a modular architecture that reconstructs and/or forecasts complete spatiotemporal dynamics from sparse sensor observations confined to short temporal windows. LAPIS-SHRED operates through a three-stage pipeline: (i) a SHRED model is pre-trained entirely on simulation data to map sensor time-histories into a structured latent space, (ii) a temporal sequence model, trained on simulation-derived latent trajectories, learns to propagate latent states forward or backward in time to span unobserved temporal regions from short observational time windows, and (iii) at deployment, only a short observation window of hyper-sparse sensor measurements from the true system is provided, from which the frozen SHRED model and the temporal model jointly reconstruct or forecast the complete spatiotemporal trajectory. The framework supports bidirectional inference, inherits data assimilation and multiscale reconstruction capabilities from its modular structure, and accommodates extreme observational constraints including single-frame terminal inputs. We evaluate LAPIS-SHRED on six experiments spanning complex spatio-temporal physics: turbulent flows, multiscale propulsion physics, volatile combustion transients, and satellite-derived environmental fields, highlighting a lightweight, modular architecture suited for operational settings where observation is constrained by physical or logistical limitations.

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure fields. However, scaling such models to large spatiotemporal domains is hindered by computational bottlenecks and optimization instabilities. In this work, we propose a robust distributed PINNs framework designed for efficient flow reconstruction via spatiotemporal domain decomposition. A critical challenge in such distributed solvers is pressure indeterminacy, where independent sub-networks drift into inconsistent local pressure baselines. We address this issue through a reference anchor normalization strategy coupled with decoupled asymmetric weighting. By enforcing a unidirectional information flow from designated master ranks where the anchor point lies to neighboring ranks, our approach eliminates gauge freedom and guarantees global pressure uniqueness while preserving temporal continuity. Furthermore, to mitigate the Python interpreter overhead associated with computing high-order physics residuals, we implement a high-performance training pipeline accelerated by CUDA graphs and JIT compilation. Extensive validation on complex flow benchmarks demonstrates that our method achieves near-linear strong scaling and high-fidelity reconstruction, establishing a scalable and physically rigorous pathway for flow reconstruction and understanding of complex hydrodynamics.

Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators.

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of $2.70 \times 10^{-4}$, compared with $4.02 \times 10^{-4}$ for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

Continuous approximations of flow data are useful for downstream analysis, differentiation, and visualization, but purely data-driven reconstructions do not, in general, preserve the governing physics. This limitation becomes particularly important when input data are physically inconsistent, whether due to low-fidelity discretizations or unmodeled discrepancies. In such cases, reconstructed fields may exhibit inaccurate PDE residuals, violated balance laws, or unreliable derived quantities. To address this, we propose a physics-informed B-spline framework that embeds physical constraints directly into the reconstruction process. The method constructs compact, continuously differentiable representations of discrete fields using tensor-product B-splines and determines spline control points by solving an optimization problem balancing data fidelity with residuals of the governing PDEs, alongside initial and boundary conditions. Leveraging exact analytical derivatives of the B-spline basis enables efficient and accurate evaluation of physical residuals without storing full-resolution fields. We refer to this approach as physics-informed multivariate functional approximation (PI-MFA). Numerical studies on the 1D convection-diffusion, 2D coupled Burgers, and 2D incompressible Navier-Stokes equations show PI-MFA reduces PDE residuals and improves global balance-law consistency. Compared with standard and regularized MFA, PI-MFA produces more physically faithful reconstructions and, for physically inconsistent data, lower approximation errors, while offering computational advantages over tested physics-informed neural networks. Overall, PI-MFA preserves the compactness, local support, and exact differentiability of classical spline spaces while producing reliable continuous flow fields for scientific analysis and visualization.

This work presents a high-fidelity computational fluid dynamics (CFD) and data-driven modeling framework for assembly-level flow characterization in a four-loop pressurized water reactor (PWR). A full lower-plenum and core-inlet domain was constructed using publicly available geometry and operating conditions, enabling transient simulations with pump-induced swirl boundary conditions. The results show that cold-leg swirl and lower-plenum transport generate strongly heterogeneous assembly-wise inlet flow distributions, particularly near the lower core region, while axial resistance and mixing progressively homogenize the flow at higher elevations. These physics-informed datasets were subsequently used to evaluate machine learning (ML) applications for partial field reconstruction and short-term autoregressive prediction. A 3D convolutional-based inpainting model successfully recon-structed missing assembly-level mass flow rates from partial observations, with errors concentrated in the highly turbulent base (bottom) layer and diminishing significantly in upper layers. Comparative analysis across multiple ML models demon-strates that spatially aware architectures, particularly ConvLSTM, significantly outperform sequence-based (LSTM) and operator-learning (DeepONet) approaches by effectively capturing coupled spatio-temporal dynamics. The study also high-lights key challenges, including the sensitivity of inlet flow predictions to turbulence and mesh resolution, as well as the absence of full-scale experimental validation data. Despite these limitations, the results remain consistent with expected physical behavior. Overall, this work establishes high-fidelity CFD as a critical foundation for developing data-driven surrogates, sparse sensing strategies, and future multiphysics coupling frameworks.

Accurate reconstruction of atmospheric wind fields is essential for applications such as weather forecasting, hazard prediction, and wind energy assessment, yet conventional instruments leave spatio-temporal gaps within the lower atmospheric boundary layer. Unmanned aircraft systems (UAS) provide flexible in situ measurements, but individual platforms sample wind only along their flight trajectories, limiting full wind-field recovery. This study presents a framework for reconstructing four-dimensional atmospheric wind fields using measurements obtained from a coordinated UAS swarm. A synthetic turbulence environment and high-fidelity multirotor simulation are used to generate training and evaluation data. Local wind components are estimated from UAS dynamics using a bidirectional long short-term memory network (Bi-LSTM) and assimilated into a physics-informed neural network (PINN) to reconstruct a continuous wind field in space and time. For local wind estimation, the bidirectional LSTM achieves root-mean-square errors (RMSE) of 0.064 and 0.062 m/s for the north and east components in low-wind conditions, increasing to 0.122 to 0.129 m/s under moderate winds and 0.271 to 0.273 m/s in high-wind conditions, while the vertical component exhibits higher error, with RMSE values of 0.029 to 0.091 m/s. The physics-informed reconstruction recovers the dominant spatial and temporal structure of the wind field up to 1000 m altitude while preserving mean flow direction and vertical shear. Under moderate wind conditions, the reconstructed mean wind field achieves an overall RMSE between 0.118 and 0.154 m/s across evaluated UAS configurations, with the lowest error obtained using a five-UAS swarm. These results demonstrate that coordinated UAS measurements enable accurate and scalable four-dimensional wind-field reconstruction without dedicated wind sensors or fixed infrastructure.

We develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using background-oriented schlieren (BOS) measurements and physics-informed reconstruction. Our framework utilizes a light projector that projects a pattern onto a target back-wall and a camera that observes small distortions in the light pattern. While the single-view BOS tomography problem is severely ill-posed, our proposed framework addresses this using: (1) improved ray tracing, (2) a physics-based light rendering approach and loss formulation, and (3) a physics-based regularization using a physics-informed neural network (PINN) to ensure that the reconstructed airflow is consistent with the governing equations for buoyancy-driven flows.

Traditional Predictive Digital Twins often remain geometrically rigid, requiring extensive retraining or fine-tuning whenever the underlying physical domain or boundary conditions change. To overcome this limitation, we present a novel framework for \textit{Zero-Shot Digital Twins} that seamlessly couples real-time visual perception with a geometry-agnostic, physics-informed reasoning engine. At the core of our architecture is the Thermodynamics-Informed Graph Neural Network architecture, a Geometric Deep Learning solver grounded in a metriplectic thermodynamic formalism that enforces energy conservation and non-negative entropy production locally through graph message passing. The framework integrates an auxiliary Graph Neural Network to infer unobservable fields (such as stress tensors or velocity and energy distributions) directly from sparse initial visual boundaries, mitigating numerical start-up transients. To bridge the sim-to-real gap, we implement a continuous closed-loop data assimilation mechanism; the pipeline tracks macroscopic deformations and free-surface fluid boundaries in real-time using deep segmentation networks combined with sparse optical flow, dynamically correcting the autoregressive simulation rollout and eliminating numerical drift. To test the validity of our approach, we demonstrate the extreme generalization capabilities of our approach across two disparate physical regimes: the large deformations of a viscoelastic beam and the non-linear sloshing of a viscous fluid. In both scenarios, the unified framework instantiates physically accurate simulations on novel, unseen geometries without case-specific retraining, operating well within real-time latency budgets (approximately 25 ms per frame) and enabling the direct projection of latent mechanical variables via Augmented Reality.

Urban flow and air-quality simulations generate high-dimensional datasets describing velocity and pollutant transport across multiple spatial, temporal, and physical-variable dimensions. Reconstructing these fields from sparse sensor measurements is a fundamental challenge in environmental monitoring, digital twins, forecasting, and data assimilation. Existing low-cost reconstruction approaches are commonly based on matrix decompositions, which require multidimensional datasets to be flattened into two-dimensional snapshot matrices, thereby discarding important structural information. This work introduces the low-cost High-Order Singular Value Decomposition (lcHOSVD), a novel tensor-based sparse-sensing reconstruction framework for high-dimensional environmental fields. To the authors'knowledge, this is the first methodology that combines sparse sensing and HOSVD for field reconstruction. Unlike matrix-based approaches, lcHOSVD preserves the natural tensor structure of the data, enabling the exploitation of correlations across spatial, temporal, and physical-variable dimensions while substantially reducing the computational requirements of conventional HOSVD. The methodology is applied to urban flow and air-quality datasets, where three-dimensional velocity and pollutant concentration fields are reconstructed using only 1-4% of the available spatial locations. While lcSVD provides larger computational speed-ups, lcHOSVD consistently achieves lower reconstruction errors in configurations characterized by strong multidimensional coupling and heterogeneous dynamics across dimensions. Additional sensor-anisotropy analyses demonstrate that the tensor formulation is significantly more robust to uneven sensor distributions, a common situation in practical environmental monitoring networks.

Lagrangian data assimilation aims to recover hidden Eulerian flow fields from sparse, indirect observations of moving tracers. This problem is challenging because tracer trajectories are nonlinearly coupled with the underlying flow, making posterior inference computationally intractable in realistic, high-dimensional systems. In this work, we develop a Lagrangian conditional Gaussian Koopman network (LaCGKN), a structure-preserving, data-driven framework for joint data assimilation and prediction from Lagrangian observations. LaCGKN embeds Eulerian flow dynamics into a low-dimensional latent space governed by a nonlinear stochastic system with conditional Gaussian structure, enabling analytic posterior updates without ensemble forecasting. Unlike existing conditional Gaussian Koopman formulations that assume direct Eulerian observations, the Lagrangian setting imposes additional demands on the latent representation, which must simultaneously encode the flow dynamics and mediate nonlinear tracer-flow interactions. To address these challenges, the LaCGKN incorporates three key components: (i) tracer homogenization to enforce permutation equivariance and generalize across varying numbers of tracers; (ii) Fourier positional encoding to capture spatial dependence and reconstruct local flow features at moving tracer locations; and (iii) an SVD-inspired low-rank parameterization of the latent transition operator, which reduces model complexity while retaining expressiveness. An application to a two-layer quasi-geostrophic flow with surface tracer observations shows that LaCGKN achieves accurate and efficient Lagrangian data assimilation and prediction, without reliance on ensemble methods or the governing physical model. These results establish the LaCGKN as a unified and computationally tractable alternative to both traditional model-based approaches and purely black-box data-driven methods.

Super-resolution of geophysical fields presents unique challenges beyond natural image enhancement: fine-scale structures must respect physical dynamics, conserve mass and energy, and evolve coherently in time. These constraints are especially critical for extreme events, where rare, localized, high-intensity features drive impacts and where temporally inconsistent"hallucinated"detail can misrepresent hazards. We introduce CASCADE (Cross-scale Advective Super-resolution with Climate Assimilation and Downscaling Evolution), a framework that reframes spatiotemporal super-resolution as an explicit transport process across scales. Rather than hallucinating high-frequency content per pixel, CASCADE reconstructs fine structure by iteratively advecting coarse information along learned, flow-conditioned velocity fields through semi-Lagrangian warping. The architecture decomposes motion into resolved (large-scale) and subgrid (unresolved) components, mirroring the closure problem in numerical weather prediction, and enforces low-resolution consistency through an assimilation-style innovation step. Evaluated on SEVIR radar data for 4x super-resolution of severe convective storms, CASCADE outperforms strong baselines across both continuous metrics (PSNR, SSIM, MAE) and threshold-based skill scores (CSI, HSS, POD) while providing interpretable diagnostics through visualizable velocity and correction fields. By encoding advection as the fundamental operator rather than learning it implicitly, CASCADE produces temporally coherent, physically consistent, and mass-conserving reconstructions well suited to advection-dominated extremes in atmospheric and oceanic applications.

In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the flow field can be achieved using observations available only in a subregion of the domain, possibly far from the boundary. We focus on the two-dimensional incompressible Navier-Stokes equations posed in a bounded physical domain with Dirichlet boundary conditions. Building on the continuous data assimilation framework of Azouani, Olson, and Titi (2014), we rigorously prove that the assimilated solution converges globally to the true solution under suitable conditions on the nudging parameter, spatial resolution, and the geometry of the observation region, specifically, when the maximum distance from any point in the domain to the observational subregion is bounded by a constant multiple of \( \nu^{1/2} \) (in terms of scaling). Our computational results, conducted via finite element methods over complex geometries, support the theoretical findings and reveal even greater robustness in practice. Specifically, synchronization with the true solution is achieved even when the observational subregion lies farther from the rest of the domain than the theoretical threshold permits. Across all three tested scenarios, the local nudging algorithm performs comparably to full-domain assimilation, reaching global accuracy up to machine precision. Interestingly, observational data near the boundary are found to be largely uninformative. This demonstrates that full observability is not necessary: carefully chosen interior observations, even far from the boundary, can suffice.

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization to held-out mesh geometries, wind directions, and sensor configurations within the studied urban-flow setting, without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

This paper presents an innovative Reduced-Order Model (ROM) for merging experimental and simulation data using Data Assimilation (DA) to estimate the"True"state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach implementing the Ensemble Kalman Filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost Singular Value Decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through the LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, the LR approach with a compression rate of 15.9 can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low Relative Root Mean Square Error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it suitable for large-scale and real-time applications, such as environmental monitoring or aerospace.

A data-driven investigation of the flow around a high-rise building is performed combining heterogeneous experimental samples and RANS CFD. The coupling is performed using techniques based on the Ensemble Kalman Filter (EnKF), including advanced manipulations such as localization and inflation. The augmented state estimation obtained via EnKF has also been employed to improve the predictive features of the model via an optimization of the five free global model constant of the $\mathcal{K}-\varepsilon$ turbulence model used to close the equations. The optimized values are very far from the classical values prescribed as general recommendations and implemented in codes, but also different from other data-driven analyses reported in the literature. The results obtained with this new optimized parametric description show a global improvement for both the velocity field and the pressure field. In addition, some topological improvement for the flow organization are observed downstream, far from the location of the sensors.

We present TURB-Rot, a new open database of 3d and 2d snapshots of turbulent velocity fields, obtained by Direct Numerical Simulations (DNS) of the original Navier-Stokes equations in the presence of rotation. The aim is to provide the community interested in data-assimilation and/or computer vision with a new testing-ground made of roughly 300K complex images and fields. TURB-Rot data are characterized by multi-scales strongly non-Gaussian features and rough, non-differentiable, fields over almost two decades of scales. In addition, coming from fully resolved numerical simulations of the original partial differential equations, they offer the possibility to apply a wide range of approaches, from equation-free to physics-based models. TURB-Rot data are reachable at this http URL

We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hidden quantities of interest such as velocity and pressure fields merely from spatio-temporal visualizations of a passive scaler (e.g., dye or smoke), transported in arbitrarily complex domains (e.g., in human arteries or brain aneurysms). Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions. This makes HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce. The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information (e.g., lift and drag forces or wall shear stresses in arteries) for which direct measurements may not be possible.

High frame-rate RGB-D videos are crucial for a variety of downstream tasks, including motion analysis, dynamic scene understanding, and 3D reconstruction. However, due to hardware and sensing constraints, practical RGB-D cameras are typically limited to low frame rates, making it difficult to capture rapid scene dynamics. Existing video interpolation methods have achieved strong performance on RGB data, but they are not readily applicable to RGB-D scenarios, where they often yield blurry boundaries, visible artifacts, and degraded geometric consistency. Furthermore, motion estimation from only two boundary frames is inherently under-constrained in complex dynamic scenes. Event cameras, by contrast, provide asynchronous measurements with ultra-high temporal resolution, offering dense motion cues. In this paper, we propose a unified multimodal framework for RGB-D video interpolation that jointly exploits RGB appearance, depth geometry, and event-based temporal cues. Specifically, it first extracts and fuses RGB, depth and event cues, then estimates bidirectional flow with motion basis refinement for RGB and Z-axial refinement for depth, and finally synthesizes the target RGB-D frame via bidirectional warping and soft blending. In addition, we construct a new RGB-D-Event dataset to alleviate the scarcity of tri-modal training data. Extensive experiments on a public benchmark and the proposed dataset demonstrate that our method achieves superior photometric fidelity for RGB interpolation and stronger geometric accuracy for depth interpolation than existing approaches.

Video frame interpolation aims to synthesize realistic intermediate frames between given endpoints while adhering to specific motion semantics. While recent generative models have improved visual fidelity, they predominantly operate in a unidirectional manner, lacking mechanisms to self-verify temporal consistency. This often leads to motion drift, directional ambiguity, and boundary misalignment, especially in long-range sequences. Inspired by the principle of temporal cycle-consistency in self-supervised learning, we propose a novel bidirectional framework that enforces symmetry between forward and backward generation trajectories. Our approach introduces learnable directional tokens to explicitly condition a shared backbone on temporal orientation, enabling the model to jointly optimize forward synthesis and backward reconstruction within a single unified architecture. This cycle-consistent supervision acts as a powerful regularizer, ensuring that generated motion paths are logically reversible. Furthermore, we employ a curriculum learning strategy that progressively trains the model from short to long sequences, stabilizing dynamics across varying durations. Crucially, our cyclic constraints are applied only during training; inference requires a single forward pass, maintaining the high efficiency of the base model. Extensive experiments show that our method achieves state-of-the-art performance in imaging quality, motion smoothness, and dynamic control on both 37-frame and 73-frame tasks, outperforming strong baselines while incurring no additional computational overhead.

Missing data is a common challenge in spatiotemporal systems, arising in applications such as air quality monitoring and urban traffic management. Traditional machine learning approaches, like recurrent and graph neural networks, rely on iterative propagation, which tends to accumulate errors over time and space. Recent diffusion-based methods mitigate error propagation but require iterative sampling and often depend on problem-agnostic Gaussian priors, limiting both efficiency and effectiveness. To address these limitations, we propose GiFlow, a Graph-Informed Flow Matching framework for spatiotemporal imputation. GiFlow replaces the typical Gaussian prior with a graph-informed prior constructed via spatiotemporal filtering of observable signals, which better aligns the source distribution to the target and thereby simplifies the generation trajectory. The flow field is parameterized by a hybrid vector field model that integrates spatial attention, temporal attention, and spatiotemporal propagation, enabling joint modeling of spatial and temporal dependencies. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed GiFlow outperforms the state-of-the-art approaches in spatiotemporal imputation. The code is available at https://github.com/zepengzhang/GiFlow.

Modeling spatial dependencies is central to spatiotemporal data analysis using Graph Neural Networks (GNNs). Traditional methods rely on distance-based kernels with predefined parameters, which restricts model capacity. Although generic adaptive mechanisms (e.g., Graph Attention Networks) offer flexibility, they often fail to capture the underlying geometric structure, performing worse than distance-based models in data-sparse scenarios. Addressing this, we revisit the kernel parameterization problem and theoretically prove that misspecified kernel parameters introduce unavoidable approximation errors in GNNs. To overcome this, we propose AdaKernel, a simple yet effective approach that learns adaptive kernel parameters within the neural network. Unlike methods that learn graph structures from scratch, AdaKernel adopts a structure-preserving strategy that optimizes the scale of physical interactions rather than discarding them. Extensive experiments on Kriging, Imputation, and Forecasting demonstrate that AdaKernel consistently improves various GNN architectures and outperforms model-agnostic adaptive baselines, validating that accurately learned kernel parameters are superior to both fixed priors and fully latent graph structures.

Spatiotemporal data analysis is pivotal across various domains, such as transportation, meteorology, and healthcare. The data collected in real-world scenarios are often incomplete due to device malfunctions and network errors. Spatiotemporal imputation aims to predict missing values by exploiting the spatial and temporal dependencies in the observed data. Traditional imputation approaches based on statistical and machine learning techniques require the data to conform to their distributional assumptions, while graph and recurrent neural networks are prone to error accumulation problems due to their recurrent structures. Generative models, especially diffusion models, can potentially circumvent the reliance on inaccurate, previously imputed values for future predictions; However, diffusion models still face challenges in generating stable results. We propose to address these challenges by designing conditional information to guide the generative process and expedite the training process. We introduce a conditional diffusion framework called C$^2$TSD, which incorporates disentangled temporal (trend and seasonality) representations as conditional information and employs contrastive learning to improve generalizability. Our extensive experiments on three real-world datasets demonstrate the superior performance of our approach compared to a number of state-of-the-art baselines.

The analysis of spatiotemporal data is increasingly utilized across diverse domains, including transportation, healthcare, and meteorology. In real-world settings, such data often contain missing elements due to issues like sensor malfunctions and data transmission errors. The objective of spatiotemporal imputation is to estimate these missing values by understanding the inherent spatial and temporal relationships in the observed multivariate time series. Traditionally, spatiotemporal imputation has relied on specific, intricate architectures designed for this purpose, which suffer from limited applicability and high computational complexity. In contrast, our approach integrates pre-trained large language models (LLMs) into spatiotemporal imputation, introducing a groundbreaking framework, GATGPT. This framework merges a graph attention mechanism with LLMs. We maintain most of the LLM parameters unchanged to leverage existing knowledge for learning temporal patterns, while fine-tuning the upper layers tailored to various applications. The graph attention component enhances the LLM's ability to understand spatial relationships. Through tests on three distinct real-world datasets, our innovative approach demonstrates comparable results to established deep learning benchmarks.

Large-scale data missing is a challenging problem in Intelligent Transportation Systems (ITS). Many studies have been carried out to impute large-scale traffic data by considering their spatiotemporal correlations at a network level. In existing traffic data imputations, however, rich semantic information of a road network has been largely ignored when capturing network-wide spatiotemporal correlations. This study proposes a Graph Transformer for Traffic Data Imputation (GT-TDI) model to impute large-scale traffic data with spatiotemporal semantic understanding of a road network. Specifically, the proposed model introduces semantic descriptions consisting of network-wide spatial and temporal information of traffic data to help the GT-TDI model capture spatiotemporal correlations at a network level. The proposed model takes incomplete data, the social connectivity of sensors, and semantic descriptions as input to perform imputation tasks with the help of Graph Neural Networks (GNN) and Transformer. On the PeMS freeway dataset, extensive experiments are conducted to compare the proposed GT-TDI model with conventional methods, tensor factorization methods, and deep learning-based methods. The results show that the proposed GT-TDI outperforms existing methods in complex missing patterns and diverse missing rates. The code of the GT-TDI model will be available at https://github.com/KP-Zhang/GT-TDI.

Missing data in time-series analysis poses significant challenges, affecting the reliability of downstream applications. Imputation, the process of estimating missing values, has emerged as a key solution. This paper introduces BRATI, a novel deep-learning model designed to address multivariate time-series imputation by combining Bidirectional Recurrent Networks and Attention mechanisms. BRATI processes temporal dependencies and feature correlations across long and short time horizons, utilizing two imputation blocks that operate in opposite temporal directions. Each block integrates recurrent layers and attention mechanisms to effectively resolve long-term dependencies. We evaluate BRATI on three real-world datasets under diverse missing-data scenarios: randomly missing values, fixed-length missing sequences, and variable-length missing sequences. Our findings demonstrate that BRATI consistently outperforms state-of-the-art models, delivering superior accuracy and robustness in imputing multivariate time-series data.

Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting the potential benefits that inter-series information could provide, such as reducing uncertainty and memorization effect. To bridge this gap, we propose PRIME, a Prototype Recurrent Imputation ModEl, which integrates both intra-series and inter-series information for imputing missing values in irregularly sampled time series. Our framework comprises a prototype memory module for learning inter-series information, a bidirectional gated recurrent unit utilizing prototype information for imputation, and an attentive prototypical refinement module for adjusting imputations. We conducted extensive experiments on three datasets, and the results underscore PRIME's superiority over the state-of-the-art models by up to 26% relative improvement on mean square error.

Multivariate time-series data are used in many classification and regression predictive tasks, and recurrent models have been widely used for such tasks. Most common recurrent models assume that time-series data elements are of equal length and the ordered observations are recorded at regular intervals. However, real-world time-series data have neither a similar length nor a same number of observations. They also have missing entries, which hinders the performance of predictive tasks. In this paper, we approach these issues by presenting a model for the combined task of imputing and predicting values for the irregularly observed and varying length time-series data with missing entries. Our proposed model (Bi-GAN) uses a bidirectional recurrent network in a generative adversarial setting. The generator is a bidirectional recurrent network that receives actual incomplete data and imputes the missing values. The discriminator attempts to discriminate between the actual and the imputed values in the output of the generator. Our model learns how to impute missing elements in-between (imputation) or outside of the input time steps (prediction), hence working as an effective any-time prediction tool for time-series data. Our method has three advantages to the state-of-the-art methods in the field: (a) single model can be used for both imputation and prediction tasks; (b) it can perform prediction task for time-series of varying length with missing data; (c) it does not require to know the observation and prediction time window during training which provides a flexible length of prediction window for both long-term and short-term predictions. We evaluate our model on two public datasets and on another large real-world electronic health records dataset to impute and predict body mass index (BMI) values in children and show its superior performance in both settings.