Machine learning/beam optics/optical correction/beam tuning

Abstract Magnetic field errors and misalignments cause optics perturbations, which can lead to machine safety issues and performance degradation. The correlation between magnetic errors and deviations of the measured optics functions from design can be used in order to build supervised learning models able to predict magnetic errors directly from a selection of measured optics observables. Extending the knowledge of errors in individual magnets offers potential improvements of beam control by including this information into optics models and corrections computation. Besides, we also present a technique for denoising and reconstruction of measurements data, based on autoencoder neural networks and linear regression. We investigate the usefulness of supervised machine learning algorithms for beam optics studies in a circular accelerator such as the LHC, for which the presented method has been applied in simulated environment, as well as on experimental data.

The application of machine learning methods and concepts of artificial intelligence can be found in various industry and scientific branches. In Accelerator Physics the machine learning approach has not found a wide application yet. This paper is devoted to evaluation of machine learning methods aiming to improve the optics measurements and corrections at LHC. The main subjects of the study are devoted to recognition and analysis of faulty beam position monitors and prediction of quadrupole errors using clustering algorithms, decision trees and artificial neural networks. The results presented in this paper clearly show the suitability of machine learning methods for the optics control at LHC and the potential for further investigation on appropriate approaches.

The field of artificial intelligence is driven by the goal to provide machines with human-like intelligence. However modern science is currently facing problems with high complexity that cannot be solved by humans in the same timescale as by machines. Therefore there is a demand on automation of complex tasks. To identify the category of tasks which can be performed by machines in the domain of optics measurements and correction on the Large Hadron Collider (LHC) is one of the central research subjects of this thesis. The application of machine learning methods and concepts of artificial intelligence can be found in various industry and scientific branches. In High Energy Physics these concepts are mostly used in offline analysis of experiments data and to perform regression tasks. In Accelerator Physics the machine learning approach has not found a wide application yet. Therefore potential tasks for machine learning solutions can be specified in this domain. The appropriate methods and their suitability for given requirements are to be investigated. The general question of this thesis is to identify the opportunities to apply machine learning methods to find and correct the errors in LHC optics and also to speed up beam measurements.

The present research in high energy physics as well as in the nuclear physics requires the use of more powerful and complex particle accelerators to provide high luminosity, high intensity, and high brightness beams to experiments. With the increased technolo- gical complexity of accelerators, meeting the demand of experimenters necessitates a blend of accelerator physics with technology. The problem becomes severe when optimization of beam quality has to be provided in accelerator systems with thousands of free parameters including strengths of quadrupoles, sextupoles, RF voltages, etc. Machine learning methods and concepts of artificial intelligence are considered in various industry and scientific branches, and recently, these methods are used in high energy physics mainly for experiments data analysis. In Accelerator Physics the machine learning approach has not found a wide application yet, and in general the use of these methods is carried out without a deep understanding on their effectiveness with respect to more traditional schemes or other alternative approaches. The purpose of this PhD research is to investigate the methods of machine learning applied to accelerator optimization, accelerator control and in particular on optics measurements and corrections. Optics correction, maximization of acceptance, and simultaneous control of various accelerator components such as focusing magnets is a typical accelerator scenario. The effectiven- ess of machine learning methods in a complex system such as the Large Hadron Collider, which beam dynamics exhibits nonlinear response to machine settings is the core of the study. This work presents successful application of several machine learning techniques such as clustering, decision trees, linear multivariate models and neural networks to beam optics measurements and corrections at the LHC, providing the guidelines for incorporation of machine learning techniques into accelerator operation and discussing future opportunities and potential work in this field.

Machine learning techniques have been used extensively in several domains of Science and Engineering for decades. These powerful tools have been applied also to the domain of high-energy physics, in the analysis of the data from particle collisions, for years already. Accelerator physics, however, has not started exploiting machine learning until very recently. Several activities are flourishing in this domain, in view of providing new insights to beam dynamics in circular accelerators, in different laboratories worldwide. This is, for instance, the case for the CERN Large Hadron Collider, where since a few years exploratory studies are being carried out. A broad range of topics have been addressed, such as anomaly detection of beam position monitors, analysis of optimal correction tools for linear optics, optimisation of the collimation system, lifetime and performance optimisation, and detection of hidden correlations in the huge data set of beam dynamics observables collected during the LHC Run 2. Furthermore, very recently, machine learning techniques are being scrutinised for the advanced analysis of numerical simulations data, in view of improving our models of dynamic aperture evolution.

With the advent of Machine Learning a few decades ago, Science and Engineering have had new powerful tools at their disposal. Particularly in the domain of particle physics, Machine Learning techniques have become an essential part in the analysis of data from particle collisions. Accelerator physics, however, only recently discovered the possibilities of using these tools to improve its analysis. In different laboratories worldwide, several activities are being carried out, typically in view of providing new insights to beam dynamics in circular accelerators. This is, for instance, the case for the CERN Large Hadron Collider, where, since a few years, exploratory studies are being carried out, covering a broad range of topics. These include the optimisation of the collimation system, the anomaly detection of beam position monitors, analysis of optimal correction tools for linear optics, lifetime and performance optimisation, and detection of hidden correlations in the huge data set of beam dynamics observables collected during the LHC Run 2. Furthermore, very recently, ML techniques are being scrutinised for the advanced analysis of numerical simulations data, in view of improving our models of dynamic aperture evolution.

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The emittance of a particle beam is a critically important parameter for many particle accelerator applications. Its measurements guide the initial tuning of an accelerator and are typically done using quadrupole or wire scans. Quadrupole scans are time-intensive, and it can be difficult to determine scan values that provide a good emittance measurement. To address this issue, we describe an adaptive quadrupole scan method that automates the determination of the scan range. With a given initial set of scanning values, our method adapts the range to capture the waist of the beam, and returns the Twiss parameters and a measure of the beam matching at the measurement screen. With the added capability to repeat beam size measurements when needed, this method provides a reliable measurement of the emittance even with sub-optimal initial conditions. To efficiently integrate these measurements into Python-based machine learning optimizations, the method was developed into a Python package, PyEmittance, at the SLAC National Accelerator Laboratory. We present the experimental tests of PyEmittance as performed at the Linac Coherent Light Source (LCLS) and the Facility for Advanced Accelerator Experimental Test (FACET-II).

The Linac coherent light source x-ray free-electron laser is a complex scientific apparatus which changes configurations multiple times per day, necessitating fast tuning strategies to reduce setup time for successive experiments. To this end, we employ a Bayesian approach to maximizing x-ray laser pulse energy by controlling groups of quadrupole magnets. A Gaussian process model provides probabilistic predictions for the machine response with respect to control parameters, enabling a balance of exploration and exploitation in the search for the global optimum. We show that the model parameters can be learned from archived scans, and correlations between devices can be extracted from the beam transport. The result is a sample-efficient optimization routine, combining both historical data and knowledge of accelerator physics to significantly outperform existing optimizers.

The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up anew energy frontier for exploration in 2010, it has gathered a global user community of about 9000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its instantaneous luminosity (rate of collisions) by a factor of five beyond the original design valueand the integrated luminosity (totalnumber of collisions) by a factor ten. The LHC is already a highly complexand exquisitely optimised machine so this upgrade must be carefully conceived and will require new infrastructures(underground and on surface)and over a decade to implement. The new configuration, known as High Luminosity LHC (HL-LHC), relies on a number of key innovations that push accelerator technology beyond its present limits. Among these are cutting-edge 11–12Tesla superconducting magnets, compact superconducting cavities for beam rotation with ultra-precise phase control, new technology and physical processes for beam collimation and 100 metre-long high-power superconducting links with negligible energy dissipation, all of which required several years of dedicated R&D; effort on a global international level. The present document describes the technologies and components that will be used to realise the projectand is intended to serve as the basis for the detailed engineering design of the HL-LHC.

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Generating high-quality laser-plasma accelerated electron beams requires carefully balancing a plethora of physical effects and is therefore challenging-both conceptually and in experiments. Here, we use Bayesian optimization of key laser and plasma parameters to flatten the longitudinal phase space of an ionization-injected electron bunch via optimal beam loading. We first study the concept with particle-in-cell simulations and then demonstrate it in experiments. Starting from an arbitrary set point, the plasma accelerator autonomously tunes the beam energy spread to the subpercent level at 254 MeV and 4.7 pC/MeV spectral density. Finally, we study a robust regime, which improves the stability of the laser-plasma accelerator and delivers sub-five-percent rms energy spread beams for 90% of all shots.

Applications of laser-plasma accelerators demand low energy spread beams and high-efficiency operation. Achieving both requires flattening the accelerating fields by controlled beam loading of the plasma wave. Here, we optimize the generation of an electron bunch via localized ionization injection, such that the combination of injected current profile and averaged acceleration dynamics results in optimal beam loading conditions. This enables the reproducible production of 1.2% rms energy spread bunches with 282 MeV and 44 pC at an estimated energy-transfer efficiency of ∼19%. We correlate shot-to-shot variations to reveal the phase space dynamics and train a neural network that predicts the beam quality as a function of the drive laser.

Synchrotron light sources, arguably among the most powerful tools of modern scientific discovery, are presently undergoing a major transformation to provide orders of magnitude higher brightness and transverse coherence enabling the most demanding experiments. In these experiments, overall source stability will soon be limited by achievable levels of electron beam size stability, presently on the order of several microns, which is still 1-2 orders of magnitude larger than already demonstrated stability of source position and current. Until now source size stabilization has been achieved through corrections based on a combination of static predetermined physics models and lengthy calibration measurements, periodically repeated to counteract drift in the accelerator and instrumentation. We now demonstrate for the first time how the application of machine learning allows for a physics- and model-independent stabilization of source size relying only on previously existing instrumentation. Such feed-forward correction based on a neural network that can be continuously online retrained achieves source size stability as low as 0.2 μm (0.4%) rms, which results in overall source stability approaching the subpercent noise floor of the most sensitive experiments.

With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given ``elite'' status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitness of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. The machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques toward solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design. Published by the American Physical Society 2024

Abstract In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV m −1 . Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 m. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by 50 nm-rad normalized emittances. The emittance, we note, is the effective area in transverse phase space ( x , p x / m e c ) or ( y , p y / m e c ) occupied by the beam distribution, and it is relevant to achievable beam sizes as well as setting a limit on FEL wavelength. These beams, when injected into innovative, short-period (1–10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine—including the imaging of virus particles—which may profit from this new model of performing XFEL science.

<p>A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.</p>

High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system. Typical GP models learn from past observations to make predictions, but this reduces their applicability to systems where there is limited relevant archive data. Instead, here we use a fast approximate model from physics simulations to design the GP model. The GP is then employed to make inferences from sequential online observations in order to optimize the system. Simulation and experimental studies were carried out to demonstrate the method for online control of a storage ring. Our method is a simple prescription to construct a custom GP model, including correlations between the high-dimensional input space, while encoding the physical response of a system. The ability to inform the machine-learning model with physics, without relying on the availability and range of prior data, may have wide applications in science.

Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

Optics measurements at the LHC are mainly based on turn-by-turn signal from hundreds of beam position monitors (BPMs). Faulty BPMs produce erroneous signal causing unreliable computation of optics functions. Therefore, detection of faulty BPMs prior to optics computation is crucial for adequate optics analysis. Most of the faults can be removed by applying traditional cleaning techniques. However, optics functions reconstructed from the cleaned turn-by-turn data systematically exhibit a few nonphysical values which indicate the presence of remaining faulty BPMs. A novel method based on the Isolation Forest algorithm has been developed and applied in LHC operation, allowing to significantly reduce the number of undetected faulty BPMs, thus improving the optics measurements. This report summarizes the operational results and discusses the evaluation of the developed method on simulations, including extensive studies and optimization of the preexisting cleaning technique and verification of a new method in terms of coupling measurement. The advantages of the chosen algorithm compared to some other unsupervised learning techniques are also discussed.

The output power of a free electron laser (FEL) has extremely high variance even when all FEL parameter set points are held constant because of the stochastic nature of the self-amplified spontaneous emission (SASE) FEL process, drift of thousands of coupled parameters, such as thermal drifts, and uncertainty and time variation of the electron distribution coming off of the photo cathode and entering the accelerator. In this work, we demonstrate the application of automatic, model-independent feedback for the maximization of average pulse energy of the light produced by free electron lasers. We present experimental results from both the European x-ray free electron laser at DESY and from the Linac Coherent Light Source at SLAC. We demonstrate application of the technique on rf systems for automatically adjusting the longitudinal phase space of the beam, for adjusting the phase shifter gaps between the undulators, and for adjusting steering magnets between undulator sections to maximize the FEL output power. We show that we can tune up to 105 components simultaneously based only on noisy average bunch energy measurements.

The physics reach of the LHC requires unprecedented luminosity and beam intensity in proton-proton collisions. The maximum intensity in the LHC is directly coupled to the maximum peak beam loss rate and the cleaning efficiency from the collimation system. A sophisticated LHC collimation system is implemented in two cleaning insertions and in the experimental areas. In a first phase 88 collimators are installed, being controlled by 344 stepping motors in total. The work of this PhD analyzes the achievable cleaning efficiency with realistic imperfections, defines the required collimator settings and establishes available tolerances for collimator setup and transient optics changes. An optimal setup strategy can optimize cleaning efficiency, ensure passive protection, maximize tolerances, minimize the required beam time for setup of the system and support the expected evolution in LHC beam intensity. Such an optimized strategy is described.

This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of dynamics are mapped onto the weights of a polynomial neural network. The resulting network approximates the dynamical system with perfect accuracy prior to training and provides a possibility to tune the network weights on additional experimental data. We propose a symplectic regularization approach for such polynomial neural networks that always restricts the trained model to Hamiltonian systems and significantly improves the training procedure. The proposed networks can be used for beam dynamics simulations or for fine-tuning of beam optics models with experimental data. The structure of the network allows for the modeling of large accelerators with a large number of magnets. We demonstrate our approach on the examples of the existing PETRA III and the planned PETRA IV storage rings at DESY.

Optimal tuning of particle accelerators is a challenging task. Many different approaches have been proposed in the past to solve two main problems—attainment of an optimal working point and performance recovery after machine drifts. The most classical model-free techniques (e.g., Gradient Ascent or Extremum Seeking algorithms) have some intrinsic limitations. To overcome those limitations, Machine Learning tools, in particular Reinforcement Learning (RL), are attracting more and more attention in the particle accelerator community. We investigate the feasibility of RL model-free approaches to align the seed laser, as well as other service lasers, at FERMI, the free-electron laser facility at Elettra Sincrotrone Trieste. We apply two different techniques—the first, based on the episodic Q-learning with linear function approximation, for performance optimization; the second, based on the continuous Natural Policy Gradient REINFORCE algorithm, for performance recovery. Despite the simplicity of these approaches, we report satisfactory preliminary results, that represent the first step toward a new fully automatic procedure for the alignment of the seed laser to the electron beam. Such an alignment is, at present, performed manually.

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With the advent of increased computational resources and improved algorithms, machine learning-based models are being increasingly applied to complex problems in particle accelerators. However, such data-driven models may provide overly confident predictions with unknown errors and uncertainties. For reliable deployment of machine learning models in high-regret and safety-critical systems such as particle accelerators, estimates of prediction uncertainty are needed along with accurate point predictions. In this investigation, we evaluate Bayesian neural networks (BNN) as an approach that can provide accurate predictions along with reliably quantified uncertainties for particle accelerator problems, and compare their performance with bootstrapped ensembles of neural networks. We select three accelerator setups for this evaluation: a storage ring, a photoinjector, and a linac. The problems span different data volumes and dimensionalities (e.g., scalar predictions as well as image outputs). It is found that BNN provide accurate predictions of the mean along with reliable estimates of predictive uncertainty across the test cases. In this vein, BNN may offer an attractive alternative to deterministic deep learning tools to generate accurate predictions with quantified uncertainties in particle accelerator applications.

Online tuning of particle accelerators is a complex optimisation problem that continues to require manual intervention by experienced human operators. Autonomous tuning is a rapidly expanding field of research, where learning-based methods like Bayesian optimisation (BO) hold great promise in improving plant performance and reducing tuning times. At the same time, reinforcement learning (RL) is a capable method of learning intelligent controllers, and recent work shows that RL can also be used to train domain-specialised optimisers in so-called reinforcement learning-trained optimisation (RLO). In parallel efforts, both algorithms have found successful adoption in particle accelerator tuning. Here we present a comparative case study, assessing the performance of both algorithms while providing a nuanced analysis of the merits and the practical challenges involved in deploying them to real-world facilities. Our results will help practitioners choose a suitable learning-based tuning algorithm for their tuning tasks, accelerating the adoption of autonomous tuning algorithms, ultimately improving the availability of particle accelerators and pushing their operational limits.

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This document contains recommendations for terminology in mass spectrometry. Development of standard terms dates back to 1974 when the IUPAC Commission on Analytical Nomenclature issued recommendations on mass spectrometry terms and definitions. In 1978, the IUPAC Commission on Molecular Structure and Spectroscopy updated and extended the recommendations and made further recommendations regarding symbols, acronyms, and abbreviations. The IUPAC Physical Chemistry Division Commission on Molecular Structure and Spectroscopy’s Subcommittee on Mass Spectroscopy revised the recommended terms in 1991 and appended terms relating to vacuum technology. Some additional terms related to tandem mass spectrometry were added in 1993 and accelerator mass spectrometry in 1994. Owing to the rapid expansion of the field in the intervening years, particularly in mass spectrometry of biomolecules, a further revision of the recommendations has become necessary. This document contains a comprehensive revision of mass spectrometry terminology that represents the current consensus of the mass spectrometry community.

The ILC Technology Network (ITN) was established in 2022 by the ILC International Development Team, a subcommittee of the International Committee for Future Accelerators, to advance engineering studies toward the realisation of the International Linear Collider (ILC). While the ITN work packages focus on engineering activities for the ILC, their topics are also relevant to a broad range of accelerator applications in particle physics and beyond. These work packages are being carried out now by laboratories in Asia and Europe in close collaboration. This report summarises the current status of the ITN activities.

In this manuscript, we provide a summary of accelerator design and the key challenges of the CEPC accelerator, both of which are laid out in detail in the Conceptual Design Report (CDR) released in November 2018. We also outline future directions and challenges. In the Addendum, we briefly describe the planning and the international organization of the CEPC. The next step for the CEPC team is to perform detailed technical design studies. Effective international collaboration would be crucial at this stage. This submission for consideration by the ESPP is part of our dedicated effort in seeking international collaboration and support.

This document summarizes the findings of the Accelerator Working Group (AWG) of the International Scoping Study (ISS) of a Future Neutrino Factory and super-beam Facility. The work of the group took place at three plenary meetings along with three workshops, and an oral summary report was presented at the NuFact06 workshop held at UC-Irvine in August, 2006. The goal was to reach consensus on a baseline design for a Neutrino Factory complex. One aspect of this endeavor was to examine critically the advantages and disadvantages of the various Neutrino Factory schemes that have been proposed in recent years.

Depending on the application people use time-domain or frequency-domain signals in order to measure or describe processes. First we will look at the definition of these terms, produce some mathematical background and then apply the tools to measurements made in the accelerator domain. We will first look at signals produced by a single bunch passing once through a detector (transfer line, linac), then periodic single bunch passages (circular accelerator) and at the end multi-bunch passages in a circular accelerator.

Various frameworks have been proposed to predict mechanical system responses by combining data from different fidelities for design optimization and uncertainty quantification as reviewed by Fernández-Godino et al. and Peherstorfer et al.. Among all frameworks, the Bayesian framework based on Gaussian processes has the potential of highest accuracy. However, the Bayesian framework requires optimization for estimating hyper-parameters, and there is a risk of estimating inappropriate hyper-parameters as Kriging surrogate often does, especially in the presence of noisy data. We propose an easy and yet powerful framework for practical design and applications. In this technical note, we revised a heuristic framework which minimizes the prediction errors at high-fidelity samples using optimization. The system behavior (high-fidelity behavior) is approximated by a linear combination of the low-fidelity predictions and a polynomial-based discrepancy function. The key idea is to consider the low-fidelity model as a basis function in the multi-fidelity model with the scale factor as a regression coefficient. The design matrix for least-square estimation consists of both the low-fidelity model and discrepancy function. Then the scale factor and coefficients of the basis functions are obtained simultaneously using linear regression, which guarantees the uniqueness of fitting process. Besides enabling efficient estimation of the parameters, the proposed least-squares multi-fidelity surrogate (LS-MFS) can be applicable to other regression models by simply replacing the design matrix. Therefore, the LS-MFS is expected to be easily applied to various applications such as prediction variance, D-optimal designs, uncertainty propagation and design optimization.