基于深度神经算子（DeepONet）代理驱动下的降雨边坡可靠性分析

… (DeepONet), and construct a direct mapping between the uncertain factors and their induced responses in unsaturated-slope … between variables, DeepONet primarily focuses on …

Recent advances in deep learning and artificial intelligence (AI) have significantly transformed the analysis of rock slopes and geotechnical structures. Rock slope stability is governed by complex interactions among rock mass discontinuity networks, mechanical properties, environmental loading conditions, and stress redistribution. Traditional analytical and numerical methods, including discrete element methods, finite element simulations, and limit equilibrium approaches, provide valuable insights; however, they often have limitations in capturing complex failure mechanisms and handling heterogeneous datasets. This review systematically synthesizes recent developments in AI-driven approaches for rock slope engineering, with particular emphasis on their integration with physical and numerical modeling frameworks and their role in improving the performance assessment of geotechnical systems. Key applications include machine learning-based slope stability prediction, automated discontinuity detection, surrogate modeling for numerical simulations, and spatiotemporal forecasting of slope deformation using monitoring data. The review further discusses emerging approaches such as physics-informed machine learning, digital twin systems, and hybrid AI–numerical frameworks, which combine data-driven learning with established rock mechanics principles. In addition, the potential of AI technologies to support sustainable rock slope management is evaluated, including early warning systems, optimal stabilization design, and resilient infrastructure monitoring. Finally, major challenges related to data quality, model interpretability, uncertainty, and integration with physical models are identified. The review suggests that future research should focus on integrating AI with physics-based modeling and uncertainty quantification, supported by rigorous validation strategies and high-quality datasets, to improve reliability and practical applicability in rock slope engineering. This paper provides a comprehensive perspective on how AI and deep learning can improve the understanding, prediction, and long-term management of rock slopes in modern geotechnical engineering practice.

The modeling and simulation of complex spatiotemporal systems are crucial for understanding and solving multidimensional dynamical systems, particularly in earth and environmental sciences. Accurate comprehension and computational modeling of fluid transport, environmental processes, and substance diffusion depend heavily on solving governing equations. Despite significant advancements in artificial intelligence techniques, such as deep learning and neural operator methods, challenges persist regarding robustness, scalability, and adherence to physical laws in hydrodynamic systems. This paper introduces a multi-scale interdisciplinary hybrid learning framework that integrates physics-informed neural networks with neural operator-based deep learning techniques to model hydrodynamic transport processes. By incorporating convolutional neural networks for multi-scale feature extraction and implementing hard constraints to enforce physical boundary conditions, the proposed framework enhances the stability and accuracy of predictions in dynamic fluid systems. The approach facilitates efficient reconstruction of spatiotemporal characteristics and parameterized dynamics while ensuring physical consistency. Through case studies of two-dimensional solute diffusion equations, the framework demonstrates superior generalizability and robustness in addressing high-dimensional and nonlinear fluid systems. Comparative experiments with multiple baseline models highlight significant improvements in prediction accuracy, noise resistance, and adaptability to sparse datasets. The proposed method effectively addresses limitations of traditional data-driven approaches by integrating domain-specific physical principles, providing a reliable and high-fidelity solution for hydrodynamic modeling and environmental system monitoring. This research offers a transformative approach to feature extraction, dynamic representation, and physically consistent modeling of complex spatiotemporal systems.

… This formulation enables PI-DeepONet to jointly learn the combined effects of inflow and rainfall forcings. The trunk network remains unchanged and provides t i , j ( x , y , t ) at any …

Water quality is foundational to environmental sustainability, ecosystem resilience, and public health. Deep learning offers transformative potential for large-scale water quality prediction and scientific insights generation. However, their widespread adoption in high-stakes operational decision-making, such as pollution mitigation and equitable resource allocation, is prevented by unresolved trustworthiness challenges, including performance disparity, robustness, uncertainty, interpretability, generalizability, and reproducibility. In this work, we present a multi-dimensional, quantitative evaluation of trustworthiness benchmarking three state-of-the-art deep learning architectures: recurrent (LSTM), operator-learning (DeepONet), and transformer-based (Informer), trained on 37 years of data from 482 US basins to predict 20 water quality variables. Our investigation reveals systematic performance disparities tied to process complexity, data availability, and basin heterogeneity. Management-critical variables remain the least predictable and most uncertain. Robustness tests reveal pronounced sensitivity to outliers and corrupted targets; notably, the architecture with the strongest baseline performance (LSTM) proves most vulnerable under data corruption. Attribution analyses align for simple variables but diverge for nutrients, underscoring the need for multi-method interpretability. Spatial generalization to ungauged basins remains poor across all models. This work serves as a timely call to action for advancing trustworthy data-driven methods for water resources management and provides a pathway to offering critical insights for researchers, decision-makers, and practitioners seeking to leverage artificial intelligence (AI) responsibly in environmental management.

… Deep operator networks (DeepONets), capable of learning … time series forecasting, DeepONets struggle to model the … we propose an adaptive physics-informed DeepONet (API-DONet), …

Avalanches are typical natural disasters in alpine watersheds. Near-real-time early warning and multi-scenario risk assessment require a balance between physical consistency and …

… , this study proposed a surrogate Deep Neural Operator (DeepONet) model to enhance the calibration efficiency. The surrogate DeepONet uses a branch network to project the high-…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO) have demonstrated excellent generalization properties when mapping between spatial function spaces. However, they struggle in mapping the temporal dynamics of time-dependent PDEs, especially for time steps not explicitly seen during training. This limits their temporal accuracy as they do not leverage these dynamics in the training process. In addition, most NOs tend to be prohibitively costly to train, especially for higher-dimensional PDEs. In this paper, we propose the Temporal Neural Operator (TNO), an efficient neural operator specifically designed for spatio-temporal operator learning for time-dependent PDEs. TNO achieves this by introducing a temporal-branch to the DeepONet framework, leveraging the best architectural design choices from several other NOs, and a combination of training strategies including Markov assumption, teacher forcing, temporal bundling, and the flexibility to condition the output on the current state or past states. Through extensive benchmarking and an ablation study on a diverse set of example problems we demonstrate the TNO long range temporal extrapolation capabilities, robustness to error accumulation, resolution invariance, and flexibility to handle multiple input functions.

… DeepONet architectures (vanilla DeepONet, physics-informed DeepONet (PI-DeepONet), and Markov DeepONet … Extensive numerical experiments exhibited that vanilla DeepONet …

Severe turbulence and nonlinear wind loads in mountainous wind fields make it difficult to predict the lift, drag, and torque coefficients of bridges accurately, thereby affecting the analysis of wind-resistant stability. This paper applies a deep learning framework that combines Diffusion and Fourier Neural Operator (FNO). The diffusion model is used to generate high-fidelity wind field data. FNO is used to efficiently extract spatially relevant features and achieve cross-scale generalization, thereby achieving precise modeling of the three-force coefficients. With the help of this model, the dynamic response and wind-resistant stability of bridges under complex wind fields are deeply evaluated. Based on the physical constraint training diffusion model, a conditional diffusion process is constructed on the WRF (Weather Research and Forecasting Model) large eddy simulation dataset. A three-dimensional pulsating wind speed field containing terrain disturbances is generated through latent space interpolation with a resolution of 0.1D (where D is the beam height). An eight-layer Fourier convolutional branch network is established to capture the vortex evolution law in the 0.5D-5D spatial range around the main beam through frequency domain transformation, and output a quantitative description of the detachment bubble formation position and reattachment length. FNO-ODE (Ordinary Differential Equation) is constructed, and the aerodynamic prediction results are embedded in the Newmark-β method solution process to achieve bidirectional coupling calculation of wind load and bridge torsion/vertical bending vibration mode. The time step is compressed to 0.001 s. The Hilbert spectrum characteristics of the buffeting response time history are analyzed based on the attention mechanism. The divergent vibration starting point is automatically identified, and the probability distribution of the unstable wind speed is output. The experimental results show that the displacement curve and lift frequency are both 0.5 Hz, and the bridge vibration is mainly caused by the periodic excitation of the wind load. When the Lyapunov index is equal to 0, the critical wind speed is about 45 m/s, and the wind speed greater than 60 m/s triggers flutter. The median error of Diffusion+FNO in the critical wind speed prediction is 3.9%, and the interquartile range is 2.9%–4.3%, with extremely high prediction consistency. In the range of 60° to 120° on the circumferential angle of the main beam surface, high pulsating pressure may cause local aerodynamic load mutations and aggravate the structural buffeting response.

… achieve trustworthiness utilizing Bayesian neural networks and DeepONets, which 14 … trunk net replacement by POD or feeding of the DeepONet by kernel-expanded inputs 9 …

… Time dependent reliability analysis and uncertainty … proposed DeepONet in solving time dependent reliability analysis … and deep learning algorithms, DeepONet is an operator network …

… applications in structural reliability analysis, risk assessment, … study lies in employing DeepONet as a dimension reduction … effectively mitigate vanishing gradient issues, stabilize the …

… To this end, a Hybrid-DeepONet is proposed to achieve high-… used to train the Hybrid-DeepONet model, forming a predictive … Experimental results demonstrate that Hybrid-DeepONet …

… 3) Training Procedure: The DeepONet is trained on a large dataset generated as described … (MSE) loss function with mini-batch gradient descent (implemented in PyTorch or TensorFlow…

Applications in the field of data-driven mechanics are widely studied in the last years exploiting latest development of artificial intelligence. In this context, several machine learning techniques have been adopted to offer a fast and accurate prediction of the structural response of materials and complex structural systems. A relatively new machine learning concept relies on the use of Deep Operator Networks (DeepONets) that can approximate operators accurately and efficiently, from a relatively small dataset. The article, therefore, provides the methodology framework of applying a deep operator network (DeepONet) in structural mechanics applications. A dataset is developed using parametric non-linear finite element simulations for a two-dimensional fibre-reinforced composite structure. Then, a DeepONet is developed, aiming to predict the failure response of this structure. Comparison with results obtained from traditional Artificial Neural Networks (ANNs) is also presented. Results obtained from testing the trained DeepONet model on data not included in training indicate a proper performance. Testing the DeepONet model on unseen trunk input or branch input functions leads to satisfactory accuracy, while testing it on unseen trunk and branch input leads to a decent accuracy, that is improved compared with the one received from ANNs. Thus, the capacity of DeepONet to predict the response in the context of non-linear structural mechanics is evaluated.

… 11 (b), the PI DeepONet experiences a gradient explosion around the 300th iteration, causing the loss function to become infinite and terminating the training process. …

This paper presents an integrated computational framework for predicting temperature fields in glulam beam–column connections under fire conditions, combining finite element modeling, automated parametric analysis, and deep learning techniques. A high-fidelity heat transfer finite element model was developed, incorporating the anisotropic thermal properties of wood and temperature-dependent material behavior, validated against experimental data with strong agreement. To enable large-scale parametric studies, an automated Abaqus model modification and data processing system was implemented, improving computational efficiency through the batch processing of geometric and material parameters. The extracted temperature field data was used to train a DeepONet neural network, which achieved accurate temperature predictions (with a L2 relative error of 1.5689% and an R2 score of 0.9991) while operating faster than conventional finite element analysis. This research establishes a complete workflow from fundamental heat transfer analysis to efficient data generation and machine learning prediction, providing structural engineers with practical tools for the performance-based fire safety design of timber connections. The framework’s computational efficiency enables comprehensive parametric studies and design optimizations that were previously impractical, offering significant advancements for structural fire engineering applications.

Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization and real-time control. Conventional deep learning surrogates often struggle with complex, non-parametric three-dimensional (3D) geometries and directionally varying loads. This work presents Point-DeepONet, an operator-learning-based surrogate that integrates PointNet into the DeepONet framework to learn a mapping from non-parametric geometries and variable load conditions to physical response fields. By leveraging PointNet to learn a geometric representation from raw point clouds, our model circumvents the need for manual parameterization. This geometric embedding is then synergistically fused with load conditions within the DeepONet architecture to accurately predict three-dimensional displacement and von Mises stress fields. Trained on a large-scale dataset, Point-DeepONet demonstrates high fidelity, achieving a coefficient of determination (R²) reaching 0.987 for displacement and 0.923 for von Mises stress. Furthermore, to rigorously validate its generalization capabilities, we conducted additional experiments on unseen, randomly oriented load directions, where the model maintained exceptional accuracy. Compared to nonlinear finite element analyses that require about 19.32 minutes per case, Point-DeepONet provides predictions in mere seconds-approximately 400 times faster-while maintaining excellent scalability. These findings, validated through extensive experiments and ablation studies, highlight the potential of Point-DeepONet to enable rapid, high-fidelity structural analyses for complex engineering workflows.

This study introduces the Graph-Structured Physics-Informed DeepONet (GS-PI-DeepONet), a novel neural network framework designed to address the challenges of solving parametric Partial Differential Equations (PDEs) in structural analysis, particularly for problems with complex geometries and dynamic boundary conditions. By integrating Graph Neural Networks (GNNs), Deep Operator Networks (DeepONets), and Physics-Informed Neural Networks (PINNs), the proposed method employs graph-structured representations to model unstructured Finite Element (FE) meshes. In this framework, nodes encode physical quantities such as displacements and loads, while edges represent geometric or topological relationships. The framework embeds PDE constraints as soft penalties within the loss function, ensuring adherence to physical laws while reducing reliance on large datasets. Extensive experiments have demonstrated the GS-PI-DeepONet’s superiority over traditional Finite Element Methods (FEMs) and standard DeepONets. For benchmark problems, including cantilever beam bending and Hertz contact, the model achieves high accuracy. In practical applications, such as stiffness analysis of a recliner mechanism and strength analysis of a support bracket, the framework achieves a 7–8 speed-up compared to FEMs, while maintaining fidelity comparable to FEM, with R2 values reaching up to 0.9999 for displacement fields. Consequently, the GS-PI-DeepONet offers a resolution-independent, data-efficient, and physics-consistent approach for real-time simulations, making it ideal for rapid parameter sweeps and design optimizations in engineering applications.

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure–volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator–regression neural network. This surrogate model is trained to predict the pressure–volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

This paper proposes a DeepONet-based uncertainty quantification framework for power system dynamics with stochastic loads modeled via the Ornstein-Uhlenbeck process. We model the stochastic power system using stochastic differential and algebraic equations (SDAE), which allow us to transport the stochasticity from the loads through the power system dynamics. Then, the proposed DeepONet-based framework learns a parametric surrogate for the infinite-dimensional solution operator of the SDAEs. This surrogate solution operator allows us to quantify uncertainty by mapping the stochastic response of the loads to statistical estimates of power system dynamic trajectories, which contain critical information for operators and planners. The effectiveness and scalability of our method are verified (i) using the IEEE 39-bus and the WECC 179-bus systems and (ii) by comparing it to Monte Carlo and other surrogate baselines.

Seismic travel time plays a fundamental role in a wide array of geophysical applications. Traditionally, numerical simulation of travel time involves solving the eikonal equation. However, conventional methods are typically limited to simulating the travel-time field for a single source and velocity model at a time. This limitation poses challenges, particularly when dealing with inverse problems that necessitate multiple forward simulations to infer velocity models based on travel-time data excited by different sources. In recent years, machine learning (ML) has proven its effectiveness in tackling problems associated with partial differential equations (PDEs). Among these methods, the deep operator network (DeepONet) has gained attention for its adaptable structure and minimal generalization error. In response to the challenges posed by solving the eikonal equation in heterogeneous media, we introduce a modified architecture known as the fully convolutional DeepONet (FC-DeepONet). This approach leverages convolutional operations to extract features directly from 2-D data and avoid flattening operations that could lead to the loss of important spatial information. The FC-DeepONet model takes the velocity model and source location as input and generates the corresponding travel-time fields as output. Through numerical experiments, we validate the efficacy of our proposed method in accurately predicting travel-time fields induced by sources located at various positions across diverse velocity models. Besides, our approach demonstrates robustness by providing reasonably accurate predictions even in scenarios involving velocity models with irregular topography. This adaptability holds significant promise for practical applications, particularly in cases characterized by complex geological features.

This paper proposes a surrogate model using a deep operator neural network (DeepONet) to predict transient drop motion of CR in real-time. The DeepONet model is trained using …

Forecasting monthly precipitation in mountainous terrain poses challenges that push conventional deep learning approaches to their limits: convective processes operate locally while orographic effects span entire drainage basins. We compare three architecture families on precipitation prediction across the Colombian Andes: ConvLSTM (convolutional recurrent), FNO-ConvLSTM (spectral–temporal), and GNN-TAT (graph attention LSTM). Using CHIRPS v2.0 and SRTM topography for Boyacá department (61 × 65 grid, 3965 nodes), we evaluate 39 configurations across feature bundles (BASIC, KCE elevation clusters, and PAFC autocorrelation lags) and horizons from 1 to 12 months. GNN-TAT matches ConvLSTM accuracy (R2: 0.628 vs. 0.642; RMSE: 82.29 vs. 79.40 mm) with 95% fewer parameters (∼98K vs. 2.1M). Across configurations, GNN-TAT produces a lower mean RMSE (92.12 vs. 112.02 mm; p=0.015) and a 74.7% lower variance. The explicit graph structure, with edges weighted by elevation similarity, appears to reduce sensitivity to hyperparameter choices. Pure FNO struggles with precipitation’s spatial discontinuities (R2=0.206), though adding a ConvLSTM decoder recovers much of the lost skill (R2=0.582). Elevation clustering improves GNN-TAT significantly (p=0.036) but not ConvLSTM, suggesting that feature design should match the spatial encoding paradigm. ConvLSTM achieves peak accuracy on local patterns; GNN-TAT provides robust predictions with interpretable spatial reasoning. These complementary strengths motivate stacking ensembles that combine grid-based and graph-based representations.

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in recent years, however, predicting flood extents at the street and building levels in real-time is still computationally demanding. Here we present a hybrid process-based and data-driven machine learning (ML) approach for flood extent and inundation depth prediction. We used the Fourier neural operator (FNO), a highly efficient ML method, for surrogate modeling. The FNO model is demonstrated over an urban area in Houston (Texas, U.S.) by training using simulated water depths (in 15-min intervals) from six historical storm events and then tested over two holdout events. Results show FNO outperforms the baseline U-Net model. It maintains high predictability at all lead times tested (up to 3 hrs) and performs well when applying to new sites, suggesting strong generalization skill.

Abstract. Accurate flood inundation modeling using high-resolution hydrodynamic simulations is computationally demanding, limiting their use for large-scale analysis and rapid scenario evaluation. Although machine learning surrogates have been developed, many struggle to reproduce the full spatiotemporal evolution of flood dynamics while maintaining physical consistency across spatial scales. In particular, simultaneously capturing basin-scale wave propagation and fine-scale inundation boundaries remains challenging. This study presents a multi-resolution deep learning framework for dynamic flood prediction. The approach combines a coarse-resolution neural operator that captures large-scale hydrodynamic behavior with a terrain-aware refinement module that reconstructs a fine-scale boundary structure. The framework is trained on high-fidelity two-dimensional shallow-water simulations and evaluated across riverine, dam-break, and complex floodplain systems, including tests under structured bathymetric uncertainty. Results demonstrate accurate reconstruction of continuous water depth fields, wet-dry delineation, and peak flow magnitude and timing. The model preserves the evolution of domain-integrated water volume over time, ensuring physically consistent mass dynamics rather than purely geometric agreement, and maintains probabilistic consistency when input topography is uncertain. The framework, therefore, provides high-resolution flood predictions at substantially reduced computational cost relative to direct high-resolution simulation. These findings show that multi-resolution deep learning can approximate hydrodynamic flood processes with strong physical fidelity and robustness to geometric uncertainty, supporting scalable flood hazard assessment and rapid predictive modeling.

Ensemble‐based simulation and learning (ESnL) has long been used in hydrology for parameter inference, but computational demands of process‐based ESnL can be quite high. To address this issue, we propose a deep neural operator learning approach. Neural operators are generic machine learning algorithms that can learn functional mappings between infinite‐dimensional spaces, providing a highly flexible tool for scientific machine learning. Our approach is built upon DeepONet, a specific deep neural operator, and is designed to address several common problems in hydrology, namely, model parameter estimation, prediction at ungaged locations, and uncertainty quantification. Here we demonstrate the effectiveness of our DeepONet‐based workflow using an existing large model ensemble created for an eastern U.S. watershed that is instrumented with 10 streamflow gages. Results suggest DeepONet achieves high efficiency in learning an ML surrogate model from the model ensemble, with the modified Kling‐Gupta Efficiency exceeding 0.9 on holdout test sets. Parameter inference, carried out using the trained DeepONet surrogate model and genetic algorithm, also yields robust results. Additionally, we formulate and train a separate DeepONet model for physics‐informed, seq‐to‐seq streamflow forecasting, which further reduces biases in the pre‐trained DeepONet surrogate model. While this study focuses primarily on a single watershed, our approach is general and may be extended to enable learning from model ensembles across multiple basins or models. Thus, this research represents a significant contribution to the application of hybrid machine learning in hydrology.

Accurate runoff prediction in complex slope catchments remains challenging due to terrain heterogeneity and dynamic rainfall interactions. This study conducts a systematic comparison between a physics-based Two-Dimensional Slope Hydrodynamic Model (TDSHM) and data-driven deep learning models (LSTM and CNN) for runoff forecasting under variable rainfall conditions. Using 214 rainfall–runoff events (2013–2023) from the Qiaotou watershed in Nanjing, China, the TDSHM integrates rainfall momentum, wind effects, and hydrodynamic principles to resolve spatiotemporal flow dynamics, while LSTM and CNN models leverage seven hydrological features for data-driven predictions. Results demonstrate that the TDSHM achieved superior accuracy, with a mean relative error of 10.77%, Nash–Sutcliffe Efficiency (NSE) of 0.801, and Mean Absolute Error (MAE) of 3.17 mm, outperforming LSTM (24.38% error, NSE = 0.751, MAE = 4.61 mm) and CNN (28.10% error, NSE = 0.506, MAE = 6.82 mm). The TDSHM’s explicit physical interpretability enabled precise simulation of vegetation-modulated runoff processes, validated against field observations (92% predictions within ±15% error). While LSTM captured temporal dependencies effectively, CNN exhibited limitations in sequential data processing. This study highlights the TDSHM’s robustness for scenarios requiring mechanistic insights and the complementary role of LSTM in data-rich environments. The findings provide critical guidance for flood risk management, soil conservation, and model selection trade-offs between physical fidelity and computational efficiency.

Rainfall-induced landslides represent a severe hazard around the world due to their sudden occurrence, as well as their widespread influence and runout distance. Considering the spatial variability of soil, stochastic analysis is often conducted to give a probability description of the runout. However, rainfall-induced landslides are complex and time-consuming for brute-force Monte Carlo analyses. Therefore, new methods are required to improve the efficiency of stochastic analysis. This paper presents a framework to investigate the influence and runout distance of rainfall-induced landslides with a two-step simulation approach. The complete process, from the initialization of instability to the post-failure flow, is simulated. The rainfall infiltration process and initialization of instability are first solved with a coupled hydro-mechanical finite element model. The post-failure flow is simulated using the coupled Eulerian–Lagrangian method, wherein the soil can flow freely in fixed Eulerian meshes. An equivalent-strength method is used to connect two steps by considering the effective stress of unsaturated soil. A rigorous method has been developed to accurately quantify the influence and runout distance via Eulerian analyses. Several simulations have been produced, using three-dimensional analyses to study the shapes of slopes and using stochastic analysis to consider uncertainty and the spatial variability of soils. It was found that a two-dimensional analysis assuming plain strain is generally conservative and safe in design, but care must be taken to interpret 2D results when the slope is convex in the longitudinal direction. The uncertainty and spatial variability of soils can lead to the statistic of influence and runout distance. The framework of using machine-learning models as surrogate models is effective in stochastic analysis of this problem and can greatly reduce computational effort.

The conventional numerical solvers for partial differential equations encounter a formidable challenge, as their computational efficiency and accuracy are heavily contingent on grid size. Recently, machine learning (ML) has exhibited substantial promise in addressing partial differential equations. Nevertheless, substantial hurdles persist in practical applications. In this work, we endeavor to establish a deep learning framework founded on the Fourier neural operator (FNO) for resolving the intricacies of simulating real landslide dynamic processes. Our findings demonstrate that the current FNO approach adeptly replicates landslide dynamic processes and boasts exceptional computational efficiency. Additionally, it is noteworthy that this data‐driven ML methodology can seamlessly incorporate data from other experimental sources or numerical simulation techniques. Consequently, this work underscores the significant potential of utilizing ML methodologies to supplant conventional numerical simulation methods.

In the U. S. Southern Great Plains (SGP) region, severe weather occurs regularly during the warm season (e.g., June–August), causing extensive property damage and loss of life. Despite advancements in observations and numerical models, estimating precipitation associated with these severe weather events remains challenging, thereby complicating accurate public warnings. Recently, machine learning (ML) models have been employed as a data‐driven approach to quantify precipitation during severe storms. In this study, we evaluate the performance of a ML model which utilizes the Fourier Neural Operator (FNO) for obtaining hourly precipitation retrievals in the SGP region. The FNO‐based model uses water vapor‐absorbing band brightness temperatures, lightning flash counts, and lightning average flash areas from NOAA's latest generation of Geostationary Operational Environmental Satellites (known as GOES‐R) as inputs to produce hourly precipitation retrievals at approximately 4‐km horizontal resolution. The “ground truth” rainfall data are hourly National Centers for Environmental Prediction (NCEP) Stage IV precipitation analysis totals. Results demonstrate that the FNO‐based model effectively generates accurate precipitation retrieval totals, offering improvements over the operational GOES‐R Quantitative Precipitation Estimation in both estimating and detecting precipitation at hourly intervals.

Global weather forecast is an important spatial-temporal prediction problem, which can provide numerous societal benefits such as extreme weather forewarning, traffic scheduling, and agricultural planning. Though many spatial-temporal prediction models have been proposed, they suffer from two drawbacks for global weather forecasts, namely 1) ignoring the physical mechanism and spherical characteristics and 2) not effectively exploiting the global and local correlations. To address the above drawbacks, in this paper, we formalize global weather state dynamics as partial differential equations (PDEs) in spherical space and infer the state of the global weather system by solving these PDEs. Specifically, we use Green’s function method to solve the PDEs and find that the solution of the spherical PDEs can be obtained by the spherical convolution. We further proposed a novel Spherical Neural Operator, SNO, which consists of spherical convolution and vanilla convolution. The former is used to solve these PDEs and model the global correlations in spherical space, and the latter is used to capture the local correlations. Upon the operator, a global weather prediction model is developed. Extensive experimental results demonstrate the effectiveness and superiority of our method over state-of-the-art approaches.

Abstract Environmental monitoring and decision‐making are sometimes hampered by missing sensor data, particularly in soil moisture (SM) records that underpin hydrological modeling, agricultural management, and climate studies. We present a novel imputation framework based on Fourier neural operators (FNO) that robustly reconstructs missing SM values by learning global spatiotemporal dependencies directly in the frequency domain. Our approach segments high‐frequency hydro‐meteorological time series into overlapping windows, incorporating rainfall, soil temperature, and normalized time coordinates and leverages spectral convolution layers with a sliding window strategy to capture both short‐ and long‐term dynamics. Through extensive experiments using multidepth SM measurements (10, 20, 30, and 40 cm), we systematically assess the impact of varying missing data ratios (from 5% to 50%) and temporal lag configurations. The FNO model demonstrates statistically better performance as compared to the traditional statistical and machine learning imputation methods. The FNO shows high correlation coefficients and low root mean square errors even under challenging rain and no‐rain conditions. Although the imputation accuracy of all models decreases during rain events, we observed that incorporating a temporal delay marginally improves performance by reducing the imputation error by up to 15%. These results establish the FNO framework as a paradigm shift in environmental data imputation, demonstrating unparalleled accuracy by harnessing global spatiotemporal dependencies to effectively overcome data sparsity even under the most challenging conditions.

… neuron (CDF probability) and one output neuron (rainfall … extremes of the wet spell slope occurs because many stations … () is the averaging operator, Var() is the variance operator and μ …

… neuron activation function ([8–12]). For example, Chen and Chen [11] adjusted both the gain and the slope … and operators by radial basis function neural networks, IEEE Transactions on …

The research into rainfall-runoff plays a very important role in water resource management. However, runoff simulation is a challenging task due to its complex formation mechanism, time-varying characteristics and nonlinear hydrological dynamic process. In this study, a nonlinear autoregressive model with exogenous input (NARX) is used to simulate the runoff in the Linyi watershed located in the northeastern part of the Huaihe river basin. In order to better evaluate the performance of NARX, a distributed hydrological model, TOPX, is used to simulate the discharge as a reference, and runoff classification by cluster analysis is used to further improve the accuracy of runoff simulation. Based on the four statistics indexes of the Nash–Sutcliffe efficiency (NSE), correlation coefficient (CC), root mean square error (RMSE) and mean relative bias (Bias), the NARX model is capable of simulating the rainfall-runoff dynamic process satisfactorily, although there is a little underestimation of the peak flow. After runoff classification, underestimation has been improved, and discharge simulation driven by NARX based on runoff classification (C-NARX) is well consistent with the observation. It is feasible to take it as a promising method, which also can be seen as a good reference and replacement for the current rainfall-runoff simulation.

… , slope, and storage characteristics of the catchment, percent of the catchment contributing runoff at the outlet at various time steps during a rainfall … , and mutation operators are applied …

… multi-task convolutional neural network model to automatically … rainfall amount based on multi-site features. Specifically, we formulate the learning task as an end-to-end multi-site neural …

… This indicates that the slope reaches the limit equilibrium state at a \(F_{r}\) of 1.23, which … neuron 4, blue points mapped by neuron 2 also appear, and both point sets extend to the slope …

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of high-dimensional, Bayesian inverse problems. Traditional solution strategies necessitate an enormous, and frequently infeasible, number of forward model solves, as well as the computation of parametric derivatives. In order to enable efficient solutions, we extend Deep Operator Networks (DeepONets) by employing a RealNVP architecture which yields an invertible and differentiable map between the parametric input and the branch-net output. This allows us to construct accurate approximations of the full posterior, irrespective of the number of observations and the magnitude of the observation noise, without any need for additional forward solves nor for cumbersome, iterative sampling procedures. We demonstrate the efficacy and accuracy of the proposed methodology in the context of inverse problems for three benchmarks: an anti-derivative equation, reaction-diffusion dynamics and flow through porous media.

… When the number of observations is small, PI-DeepONet trained with sufficiently large … than DeepONet. For the inverse problem, we incorporate PI-DeepONet in a Bayesian Markov …

This study proposes the mixed neural operator (MNO) learning framework, which further combines with the particle swarm optimization (PSO) to address challenges of solitary wave propagation over topography. The forward problem is defined as the evolution prediction of the solitary wave propagating over topography, while the inverse problem is defined as an optimization to identify the topography parameter based on the solitary wave elevation. Both the forward and inverse problems can be considered within a single framework and the dataset are provided by the classical Korteweg–de Vries (KdV) equation. The MNO framework is shown to simulate the evolution of solitary waves over topography, accurately capturing the wave elevation under different topographical conditions. By comparing with different neural operators, it is found that the U-shape neural operator is the most suitable for the KdV equation simulation. The coefficient of determination for the inverse problem based on the combination of MNO and PSO can reach 0.992, showing great potential of the approach in topography recognition. Finally, the proposed learning framework is preliminary applied to the prediction of the tsunami runup onto a complex beach, and a good agreement is also achieved between the direct simulation and the learning framework prediction.

Magnetotellurics (MT) is a powerful geophysical technique that leverages natural electromagnetic fields to characterize subsurface electrical conductivity structures. In recent years, deep neural network have shown great potential for MT data inversion. However, existing methods face inherent challenges with sparsely and irregularly sampled data sets: any variation in station layout, frequency range, or survey area extent necessitates full retraining of the network, which severely restricts their applicability to real‐world sparse and multi‐scale data sets. Here, we present a novel deep learning framework—the Reversible Deep Operator Network (RDON)—for the efficient inversion of arbitrarily sparse MT data. RDON integrates a RealNVP‐based invertible neural network into the DeepONet architecture, establishing a bijective mapping between subsurface resistivity distributions and MT responses. This mapping enables grid‐independent forward and inverse modeling within a single network. Without retraining, the architecture flexibly processes arbitrarily sparse MT data and exhibits robust generalization to unseen station distributions, frequency ranges, and model types encountered during the training phase. For scale generalization, we derive an MT‐specific scale‐invariance theorem that not only provides theoretical justification for cross‐scale generalization but also enables rigorous quantification of associated generalization errors. This allows the trained network to perform zero‐shot inference across distinct survey scales, and we further mitigate scale‐related errors via transfer learning with lightweight fine‐tuning. In addition, RDON incorporates a bootstrap resampling‐based uncertainty quantification scheme, which achieves substantial computational efficiency gains over conventional approaches. Field data application from the West Junggar region validates the reliability and practical utility of RDON under complex geological conditions.

… However, the original DeepONet … of DeepONet by utilizing Fourier layers to extract global features of the seismic traveltime in Fourier space. Then, the output of the Fourier-DeepONet is …

… DeepONet model. This procedure is then repeated to convergence. We demonstrate the Bayesian optimization with DeepONet (BO-DeepONet… gradient to perform the minimization. The …

概率反分析是推断不确定土体参数统计特征的重要手段，可以使边坡可靠度评估更接近工程实际。然而目前的概率反分析很少使用多源信息（包括监测数据、观测信息和边坡服役记录），因为这通常涉及数千个随机变量和高维似然函数的评估。因此融合多源信息对空间变异土体参数进行概率反分析进而预测降雨条件下的边坡可靠度是一项具有挑战性的难题。文章将改进的基于子集模拟的贝叶斯更新（mBUS）方法与自适应条件抽样（aCS）算法相结合，构建了空间变异土体参数概率反分析和边坡可靠度预测的框架，并以某一公路边坡为例验证了该框架的有效性。研究结果表明：通过融合多源信息所获得的土体参数后验统计特征与现场观测结果基本吻合；用更新后的土体参数预测得到2004年9月12日该边坡在暴雨工况下的失效概率为23.1%，符合实际边坡失稳情况，说明在此框架下可以充分利用多源信息解决高维概率反分析问题。

针对传统HLRF繁杂的计算过程逆可靠度在边坡工程缺少相应的几何意义解释及矿山边坡具有服务年限等问题，建立基于HLRF优化算法的矿山岩质边坡逆可靠度分析模型。首先，对边坡逆可靠度进行几何意义解释，在FLAC3D计算基础上，应用套索算法得到边坡的极限状态方程；其次，用遗传粒子群算法（GA-PSO）优化HLRF，并编写优化模型（GA-PSO-HLRF）与一次逆可靠度程序；最后，对边坡进行逆可靠度与可靠度分析，并提出考虑服务年限的边坡稳定双重指标评价方法。案例结果表明：优化模型对安全系数的反演结果为1.049，与设计安全系数1.05相差0.13%，优化模型精度较高，与一次逆可靠度结果一致；同时优化模型完成了多参数反演，可以获得较好效果；案例结果验证了逆可靠度几何意义解释；提出的双重指标评价方法有利于开展潜在边坡灾害的评估与防治。

针对京新高速公路项目在建设中遇到的裂缝、滑移、倾倒等大量边坡稳定性问题，为了探讨边坡岩土体参数与边坡稳定性间的相关关系，以及保证研究项目路段在运营期间的行车安全，实现公路网尤其是山区公路的安全、高效、便捷运行，在已有研究的基础上，分别建立了支持向量机以及附加动量因子 mc 而改进后的BP神经网络两种边坡稳定性预测模型。通过引入45个训练样本，对5个工程边坡实例的安全系数进行预测计算，分析了两种模型的平均误差和最大误差，比较了两种模型的预测精度和适用范围，并且对京新高速公路胶泥湾至冀晋界路段的工程边坡稳定性进行了预测。结果显示，样本训练阶段，支持向量机和BP神经网络两种模型均具有较高的模拟精度，而BP神经网络更优；在样本预测阶段，支持向量机的预测精度明显优于BP网络；当随着样本容量不断增大时，两种计算模型的预测精度也逐渐提高；通过结果可以得出，支持向量机预测模型有较强的外推能力和预测计算的有效性，可以更好地描述边坡稳定性复杂的非线性关系，更适用于边坡稳定性的预测分析。

为了更加快捷、高效地判定边坡稳定与否，基于机器学习，融合主成分分析法（PCA）、参数调整、影响因素权重分析等，建立了一种边坡安全稳定性评价体系。研究发现，运用PCA可以在保留80%数据原信息的前提下将输入变量维度从六维降至三维，但此时模型效果有所下降；随机森林及梯度提升(XGBoost) 两种学习算法均可搭建有效的边坡安全稳定性评估模型，通过对其预测效果的对比分析，确定XGBoost为最佳评价模型。与此同时，采取卡方检验、 F 检验以及互信息法3种相关性检验手段，并通过计算评价因子的重要程度且加以可视化展示，明确了容重、坡高、内摩擦角以及内聚力4个内在因素的重要性，最终将评估结果与实际结合提出了边坡安全防护措施。

露天矿山高边坡的变形预测是保障矿山安全生产的重要手段. 本文以西藏某矿山边坡为对象，采用高精度合成孔径干涉雷达对矿区南帮边坡进行了全天候位移监测，分析了边坡变形的基本规律；采用小波降噪理论对采集的时序位移监测数据进行了降噪处理，并且为了避免预测模型陷入局部极小值，引入遗传算法（即GA算法）整合进BP神经网络的训练步骤中，用于优化BP神经网络的初始权值和阈值设置，建立了GA–BP神经网络边坡变形时序预测模型，并与BP神经网络边坡变形时序预测模型进行对比分析. 研究结果表明： GA–BP模型较BP模型的预测精度提高了10%以上，预测的平均误差减少了50%以上，而且预测的边坡变形趋势与监测值吻合程度更高；GA–BP模型较BP模型收敛速度加快10倍以上，GA–BP模型的回归系数、模型适应度优于BP模型. 因此，采用GA–BP模型可使边坡变形预测的精度、收敛速度、泛化能力均得到提高，预测结果更为可靠，可为矿山边坡安全生产提供保障。

边坡稳定性分析是一个复杂的系统工程问题，其评价直接影响边坡工程的安全性与经济性。为了实现对边坡稳定性的快速、高效和准确评价，需要考虑边坡稳定性多种评价指标，但指标间或多或少存在一定的相关性，从而导致参量信息重叠。文章提出一种因子分析方法对边坡稳定性相关指标数据进行降维处理，提取3个综合指标对边坡稳定性进行总体评价。因子分析后的指标彼此独立，能够满足概率神经网络(PNN)样本层中采用高斯函数作径向基函数的要求。在因子分析的基础上，建立边坡稳定性评价的PNN模型，将其应用于39个典型的边坡稳定性评价。预测结果表明：5种不同的训练和测试样本个数下PNN模型仍具有良好的预测效果，其正判率分别为100%、94.87%、94.87%、84.62%和84.62%，说明因子分析与PNN模型结合可为岩土工程中边坡稳定性评价提供了一种很好的思路。

为克服单一信息源无法精确表征矿山滑坡灾害演化特征的问题，基于多源信息融合技术，从矿山边坡多源信息获取、矿山边坡多源信息融合、矿山边坡位移预测及滑坡风险评价3个方面概述了矿山边坡滑坡灾害研究进展。总结了典型的“天”“空”“地”边坡监测手段及“天−空−地”一体化协同监测方法；梳理了包含数据级、特征级和决策级融合的边坡多源信息融合流程；整理了位移与应力、位移与水文气象及其他不同类型的监测数据融合形式；阐述了基于多源信息融合的边坡位移预测及滑坡风险评价相关研究现状。基于当前矿山边坡滑坡灾害研究存在的灾害分析的准确性严重依赖监测数据质量、对岩石力学机理知识利用不足等问题，指出了矿山边坡滑坡灾害研究发展趋势：统一多源数据采集接入标准；开发监测数据与岩石力学机理融合的矿山边坡滑坡灾害分析方法；优化“天−空−地”多源信息的时空关联挖掘算法；加强基于多源信息融合的矿山边坡滑坡灾害预警平台建设。

人工智能（artificial intelligence, AI）技术近些年已经在多个学科领域中得到了广泛的应用. 在地球科学的研究中，复杂的物理过程和庞大的数据量使得传统的数据处理方法面临巨大的挑战，AI成为提高研究效率和预测精度的重要工具. 随着深度学习和神经网络技术的快速发展，AI方法能够在数据缺失或高维复杂系统中提供可行的解决方案，显著提升地球科学模型的预测准确性并加速计算过程. 在地震学、地球动力学、气候模拟、矿产资源勘探等领域，AI技术通过对大量地质、地球物理 and 环境数据的处理，帮助科学家在更短的时间内从复杂数据中提取出有价值的信息，做出更为精准的预测. 特别是物理信息神经网络的提出，进一步推动了AI在地球科学中的应用. 它结合了数据驱动和物理定律，提供了一种新颖的方式来解决传统模拟方法无法高效处理的复杂问题. 另一方面，AI技术在地球科学中的应用仍存在许多挑战，如高维数据处理、模型的可解释性、多物理场耦合问题等. 本文将综述AI，特别是深度学习与物理信息神经网络在地球科学中的应用，讨论其在各个应用领域中的优势与挑战，并展望未来的研究方向.

土质边坡系统失效概率与土体抗剪强度参数以及地下水位息息相关，在传统边坡可靠度分析中一般只考虑了土体抗剪强度参数的变异性，忽略了地下水位随机性带来的影响。该文将有限元离散技术、上限法理论、相关非高斯随机场模拟方法以及随机规划理论结合起来研究随机地下水位作用下考虑参数空间变异性的边坡系统失效概率。采用有限单元离散边坡土体，将边坡地下水位作为随机变量并考虑土体抗剪参数的空间变异性，基于塑性极限分析上限法构建边坡可靠度分析的随机规划模型；采用基于蒙特卡洛的迭代方法进行求解，得到边坡稳定性系数和速度场；根据边坡中单元的失效信息首次采用AP聚类分析方法来估算边坡的系统失效概率，发展了边坡系统可靠度分析理论。对一个经典的边坡算例进行了系统分析并与极限平衡分析方法、有限元方法结果进行对比，结果表明：随机地下水位作用下考虑参数空间变异性时，边坡存在多种失效模式，AP聚类分析方法可以根据失效单元的位置信息识别出边坡所有失效模式以及对应的失效概率；基于Matlab编制了高效的上限法并行程序，大大提高了计算效率。

降雨是诱发边坡变形失稳的主要因素，而针对降雨型边坡的预警预报也一直是工程领域的核心问题。本文将蒙特卡罗方法引入降雨型滑坡的预警预报，首先基于正态分布的岩土体物理力学参数，建立了边坡的有限元数值计算模型，并分析了9种不同型式降雨下边坡稳定性系数的变化情况。结果显示递增型降雨对边坡的稳定性尤为不利，均匀型降雨次之，递减型降雨影响最小。其次，将降雨过程划分为前期降雨+当期降雨，并确定了前期降雨对于当期降雨的有效时间为6 d。最后，论文结合可靠度理论，选取失效概率P f =10%作为预警指标，通过把前期降雨引入降雨强度-降雨历时关系曲线并作为第三坐标轴，最终将该曲线扩展成为前期降雨( A )-当期降雨( I )-降雨历时( D )曲面( A - I - D 阈值曲面)，研究结果对于降雨型边坡的预警预报具有一定的指导意义。

准确地进行非饱和土石坝坝坡可靠度分析需综合考虑土体抗剪强度参数和水力参数的空间变异性.这种多参数问题常因随机场离散的变量过多而造成维度灾难，传统分析方法难以适用.为此，提出了一种基于分片逆回归(SIR)的多元自适应回归样条(MARS)土石坝坝坡可靠度分析方法.该方法采用SIR降维，经降维后的变量矩阵通过MARS构建代理模型，进而采用蒙特卡洛模拟(MCS)评估土石坝坝坡失效概率.以某一土石坝为例，验证了所提方法的有效性，并探讨了计算结果随各参数空间变异性的变化规律，分析了滑坡规模与频率间的关系.研究结果表明：抗剪强度参数变异性对坝坡失效概率的影响大于水力参数变异性的影响；所提方法在各参数变异系数变化的情况下都能得出准确的计算结果，并有效地降低计算成本；该方法可为高维及小失效概率非饱和土石坝坝坡可靠度问题提供一条有效的途径.

目前的勘探方案预期效果评价指标常未能反映物理过程且参数较难确定.此外，勘探方案优化框架中的勘探点布置策略往往依赖位置关系并需事先确定勘探范围.为解决上述问题，以不排水抗剪强度参数为例，提出并采用安全系数的均方根误差折减率期望（expected reduction rate of the root mean square error， ERRS ）量化因融合参考勘探数据而导致的安全系数评估结果向参考安全系数集中效果的期望提升程度，并将其作为勘探方案预期效果评价的指标.此外，结合该指标和贪心算法构建了以优化勘探位置和数量为目的的勘探方案优化框架. ERRS 指标计算过程采用乔列斯基分解中点法和改进贝叶斯更新方法离散参数完全及条件随机场实现，并基于多重二阶响应面代理模型替代确定性空间变异边坡稳定性分析，有效提高指标计算精度和效率.不排水饱和黏土边坡案例显示：提出的 ERRS 指标能够在无需确定复杂参数的情况下，获得与其他指标接近的评价结果；所构建的勘探方案优化框架能够在不事先确定勘探范围的情况下，得到指定勘探数量下更优的勘探点布置，进而获得更节省成本且预期效果较好的勘探方案.提出的指标和优化框架可为实际边坡工程场地勘探方案评价及优化设计提供参考.

近年来，利用大型预训练模型来提高深度神经网络在计算机视觉以及自然语言处理等具体任务下的泛化能力和性能，逐渐成为基于深度学习的人工智能技术与应用的发展趋势. 虽然这些深度神经网络模型表现优异，但是由于模型的结构复杂、参数量庞大与计算成本极高，使得它们仍然难以被部署在如家电或智能手机等资源受限的边缘及端侧硬件平台上，这很大程度上阻碍了人工智能技术的应用. 因此，模型压缩与加速技术一直都是深度神经网络模型大规模商业化应用推广的关键问题之一. 当前在多种模型压缩与加速方案中，模型量化是其中主要的有效方法之一. 模型量化技术可以通过减少深度神经网络模型参数的位宽和中间过程特征图的位宽，从而达到压缩加速深度神经网络的目的，使量化后的网络能够部署在资源有限的边缘设备上，然而，由于量化会导致信息的大量丢失，如何在保证模型任务精度条件下实现模型量化已经成为热点问题. 另外，因硬件设备以及应用场景的不同，模型量化技术已经发展成为一个多分支的研究问题. 通过全面地调研不同角度下模型量化相关技术现状，并且深入地总结归纳不同方法的优缺点，可以发现量化技术目前仍然存在的问题，并为未来可能的发展指明方向.

通过野外调查和资料收集, 选择地形地貌、基础地质、气象水文、人类活动、岩土体性质以及植被覆盖共计18个影响因子, 基于信息量模型和卷积神经网络模型构建耦合模型对河南省济源市开展滑坡易发性评价研究, 利用GIS空间分析量化了滑坡空间分布特征. 结果表明, 研究区滑坡灾害整体呈聚集分布, 具有多个核密度高值中心; 滑坡极低、低、中、高和极高易发性区面积占比分别为45.04%、34.58%、8.67%、9.12%和2.57%. 极高和高易发区主要特征为断层发育、地质环境脆弱以及水力侵蚀. 中易发区滑坡密度最高, 为0.804个/km 2 . ROC曲线和AUC值表明评价结果准确性较好, 耦合模型预测能力具有可靠性. 滑坡影响因子敏感度分析前五位分别为距道路距离、距断层距离、坡向、地形粗糙度以及侵蚀程度和类型. 本研究可为黄土高原城镇滑坡地质灾害的预测和防治工作提供科学依据.

滑坡易发性评价是滑坡灾害管理的基础工作，也是制定各项防灾减灾措施的重要依据。针对传统的信息量模型在评价过程中确定权重值存在准确性不高的缺点，文章提出RBF神经网络和信息量耦合模型。以甘肃省岷县为研究区，筛选坡度等9个指标因子构建了滑坡灾害易发性评价指标体系，应用RBF神经网络-信息量耦合模型（RBFNN-I）进行滑坡灾害易发性评价，利用合理性检验和ROC曲线对模型的评价结果进行精度检验。结果表明：（1）RBFNN-I模型的AUC值为0.853，相比单一的RBFNN和I模型分别提高了6.3%和9.7%，说明RBFNN-I模型具有更好的评价精度；（2）岷县滑坡灾害的极高易发区和高易发区主要分布在临潭—宕昌断裂带、洮河及其支流、闾井河和蒲麻河两侧河谷地带，距断层距离、降雨量、距道路距离和NDVI是影响岷县滑坡灾害分布的主控因子。