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DOE OSTI2026

Feasibility of Correlation-Aware Inference and Universal Precision Scaling in Bonse–Hart Ultra-Small-Angle Neutron Scattering

Bonse–Hart ultra-small-angle neutron scattering (USANS) provides access to micrometre-scale structure, but useful measurements often require long counting times. In this work, we test whether the expected smoothness of the scattering profile can be exploited to improve data quality at lower counting statistics. We apply a Gaussian-process-based method to Bonse–Hart USANS data and evaluate its performance on pseudo-measurements generated from high-statistics experiments under Poisson statistics. This provides a stringent test of how well the underlying I(Q) profile can be reconstructed when the available counts are substantially reduced. We further show that, in the counting-limited regime, the reconstruction error follows a universal scaling behaviour that differs from the usual independent-counting expectation. At higher counts, the improvement crosses over to a resolution-limited regime set by analyser-angle discretization and rocking-curve width. These results clarify when correlation-aware inference is useful in USANS and provide a practical basis for improving measurement efficiency and beam-time usage.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

DOE OSTI2024

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

A machine learning degradation model for electrochemical capacitors operated at high temperature

Electrochemical capacitors (ECs) have only recently been considered as an alternative power source for telemetry sensors of drilling equipment for geothermal or oil and gas exploration. The lifecycle analysis and modelling of ECs is underrepresented in literature in comparison to other storage devices e.g. Li-ion batteries. This paper investigates the degradation of ECs when cycled outside the manufacturer-specified operating temperature envelope and proposes a machine learning-based approach for modelling the degradation. Experimental results show that end of life, defined as a 30% decrease in capacitance, occurs at 1,000 cycles when the environmental temperature exceeds the maximum operating temperature by 30%. The life-cycle test data is then used as an input to a Gaussian process regression (GPR) algorithm to predict the capacitance fade trend. The GPR is validated on a total of nine commercial cells from two different manufacturers, achieving an average root mean squared percent error of less than 2% and a mean calibration score of 93% when referenced to a 95% confidence interval. The model can be utilized to determine the EC degradation rate at a range of operating temperature values.

42 ENGINEERING↗

DOE OSTI2022

Designing Monte Carlo Simulation and an Optimal Machine Learning to Optimize and Model Space Missions

This paper investigates applying artificial intelligence (AI) algorithms to attitude control system of satellites to optimally tune the controller using high performance computing. This methodology is applied to the Virtual Telescope for X-ray Observation mission, which is a precise formation of two separate spacecraft observing multiple objects in the space in the X-ray domain. The mission is divided into phases based on the instrumentation and the mission goal. To reach an stable precise formation robust to stochastic slew and slew rate (i.e., Euler angles and angular velocities) in a minimal constrained time T , consumed energy of the attitude control system, denoted as E, and root-mean-square state error of attitude control system, denoted as e, are minimized. Monte-Carlo simulation is used for the sensitivity analysis of optimization and designing a controller. Deep neural networks (DNN), Gaussian processes (GP), and support vector regression (SVR) learn this optimization as a surrogate model, while their hyperparameters are optimized in a novel approach. THETA supercomputer at Argonne Leadership Computing Facility (ALCF) is used for optimizing the hyperparameters of DNN. The surrogate model meets the requirements of the mission, and it shows a better performance over the optimization and Monte-Carlo. The optimal DNN can satisfy the mission requirements e and T while reducing E for 90% compared to the other given methods.

42 ENGINEERING↗

DOE OSTI2026

A Machine Learning based Approach of Estimating Equivalent Circuit Model Parameters at Different SoCs of Li-ion Batteries from Voltage Relaxation

Abstract: In this study, an approach of estimating the equivalent circuit model (ECM) parameters for Li-ion batteries (LIBs) is proposed based on the voltage value at different intervals while relaxing the LIB after discharge. The typical approach for estimating ECM parameters of a LIB is to conduct electrochemical impedance spectroscopy (EIS) measurements at different frequencies and fit them to a predefined circuit model, which requires additional measuring arrangements and specialized devices. The proposed methodology utilizes four different voltages at 0s, 60s, 360s, and 1800s alongside the specific state of charge (SoC) value for a specific constant discharge current value of ~1C until the relaxation stage to train and evaluate three regression-based machine learning models— Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), and Gaussian Process Regression (GPR)—for estimating the ECM parameters of the selected model. Bayesian optimization is employed for hyperparameter tuning to achieve optimal performance for all the regressor models, among which, the GPR provided the best performance with the root-mean-squared error (RMSE) of less than 4x10-4 on average for the resistive components and less than 0.27 for capacitive components with excellent R2 scores. The simplicity of the approach enables it to eliminate the need for sophisticated measuring equipment and computation power.

Sagar, Md. Samiul [The University of Alabama (UA)]↗

DOE OSTI2023

Accelerating Scientific Simulations with Bi-Fidelity Weighted Transfer Learning

High-fidelity modeling is an essential design tool for many engineering applications. However, for complex systems, computational cost can be a limiting factor. Analyzing parameter sensitivity, uncertainty quantification, and design optimization require many model evaluations. Surrogate models are often used to develop the relationship between model parameters and quantities of interest. However, in the case of complex systems, surrogate models require several degrees of freedom and, thus, a large number of data points to determine the correct dependencies. For many applications, this may be prohibitively expensive. The reduction of computational requirements can be achieved by leveraging low-fidelity models. Low-fidelity models represent the system at a coarser resolution with the advantage of computational efficiency. Therefore, a bi-fidelity modeling paradigm, which augments the accuracy of a low-fidelity model in a computationally efficient manner by invoking limited runs of a high-fidelity model, can be leveraged to sufficiently balance the accuracy and computational requirements. In this work, a bi-fidelity weighted transfer learning method using neural networks was applied to a computational fluid dynamics heat transfer modeling problem. The transfer learning advantage was investigated as a function of hyperparameters. Our main finding is that the use of a bi-fidelity modeling paradigm achieves accuracy close to that of a high-fidelity Gaussian process model while significantly reducing computational cost. The bi-fidelity model achieves comparable performance with 90 high-fidelity samples-that is, 60% less than the samples needed to achieve similar accuracy without the use of bi-fidelity modeling,

Borowiec, Katarzyna↗

DOE OSTI2021

Multi Time-scale Imputation aided State Estimation in Distribution System

With the transition to a smart grid, we are witnessing a significant growth in sensor deployments and smart metering infrastructure in the distribution system. However, information from these sensors and meters are typically unevenly sampled at different time-scales and are incomplete. It is critical to effectively aggregate these information sources for situational awareness. In order to reconcile the heterogeneous multi-scale time-series data, we present a multi-task Gaussian process framework. This framework exploits the spatio-temporal correlation across the time-series data to impute data at any desired timescale while providing confidence bounds on the imputations. The value of the imputed data for distribution system operation is illustrated via a matrix completion based state estimation strategy. Results on the IEEE 37 bus distribution system reveals the superior performance of the proposed approach relative to linear interpolation approaches.

Dahale, Shweta↗

DOE OSTI2021

Decentralized Voltage Control of Large-Scale Distribution System with PVs Based on MADRL

This paper proposes a model-free decentralized control framework for the voltage regulation of large-scale distribution systems through the coordinated control of PV inverters. This is achieved by developing a novel interaction mechanism between the surrogate model and the centralized training and decentralized execution multiagent deep reinforcement learning framework. Specifically, the sparse Gaussian processes regression method is first utilized to develop the surrogate model of the original distribution system for reward calculation during the training stage, where each agent represents a sub-region in the centralized fashion for coordination strategy learning. After that, the learned control rules are used to inform controllers within each sub-region for real-time decisions with only local measurements. Comparative tests among various methods on the EPRI Ckt5 test system demonstrate the effectiveness of the proposed method.

distribution system↗

DOE OSTI2024

Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads

Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.

17 WIND ENERGY↗

DOE OSTI2026

Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization

We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.

Mulkin, Olivier↗

DOE OSTI2021

Enriching Load Data Using Micro-PMUs and Smart Meters

In modern distribution systems, load uncertainty can be fully captured by micro-PMUs, which can record high-resolution data; however, in practice, micro-PMUs are installed at limited locations in distribution networks due to budgetary constraints. In contrast, smart meters are widely deployed but can only measure relatively low-resolution energy consumption, which cannot sufficiently reflect the actual instantaneous load volatility within each sampling interval. In this paper, we have proposed a novel approach for enriching load data for service transformers that only have low-resolution smart meters. The key to our approach is to statistically recover the high-resolution load data, which is masked by the low-resolution data, using trained probabilistic models of service transformers that have both high- and low-resolution data sources, i.e., micro-PMUs and smart meters. The overall framework consists of two steps: first, for the transformers with micro-PMUs, a Gaussian Process is leveraged to capture the relationship between the maximum/minimum load and average load within each low-resolution sampling interval of smart meters; a Markov chain model is employed to characterize the transition probability of known high-resolution load. Next, the trained models are used as teachers for the transformers with only smart meters to decompose known low-resolution load data into targeted high-resolution load data. The enriched data can recover instantaneous load uncertainty and significantly enhance distribution system observability and situational awareness. Here, we have verified the proposed approach using real high- and low-resolution load data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

A Multi-Objective Bayesian Optimization Approach Using the Weighted Tchebycheff Method

Abstract Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard multi-objective (MO) optimization problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed MO-BO. These iteratively estimated mean utopia values are used to formulate the weighted Tchebycheff MO acquisition function. The proposed approach is implemented in two numerical test examples and one engineering design problem of optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.

Engineering↗

DOE OSTI2021

srMO-BO-3GP: A sequential regularized multi-objective Bayesian optimization for constrained design applications using an uncertain Pareto classifier

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, and latent-variable modeling, have been proposed to address the limitations of the classical BO framework. In this work, we propose a novel multi-objective BO formalism, called srMO-BO-3GP, to solve multi-objective optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GPs is assigned with a different task. The first GP is used to approximate a single-objective computed from the multi-objective definition, the second GP is used to learn the unknown constraints, and the third one is used to learn the uncertain Pareto frontier. At each iteration, a multi-objective augmented Tchebycheff function is adopted to convert multi-objective to single-objective, where the regularization with a regularized ridge term is also introduced to smooth the single-objective function. Finally, we couple the third GP along with the classical BO framework to explore the convergence and diversity of the Pareto frontier by the acquisition function for exploitation and exploration. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

42 ENGINEERING↗

DOE OSTI2022

Surrogate Modeling of Nonlinear Dynamic Systems: A Comparative Study

Surrogate models play a vital role in overcoming the computational challenge in designing and analyzing nonlinear dynamic systems, especially in the presence of uncertainty. This paper presents a comparative study of different surrogate modeling techniques for nonlinear dynamic systems. Four surrogate modeling methods, namely, Gaussian process (GP) regression, a long short-term memory (LSTM) network, a convolutional neural network (CNN) with LSTM (CNN-LSTM), and a CNN with bidirectional LSTM (CNN-BLSTM), are studied and compared. All these model types can predict the future behavior of dynamic systems over long periods based on training data from relatively short periods. The multi-dimensional inputs of surrogate models are organized in a nonlinear autoregressive exogenous model (NARX) scheme to enable recursive prediction over long periods, where current predictions replace inputs from the previous time window. Three numerical examples, including one mathematical example and two nonlinear engineering analysis models, are used to compare the performance of the four surrogate modeling techniques. The results show that the GP-NARX surrogate model tends to have more stable performance than the other three deep learning (DL)-based methods for the three particular examples studied. The tuning effort of GP-NARX is also much lower than its deep learning-based counterparts.

42 ENGINEERING↗

DOE OSTI2024

Uncertainty-Aware, Structure-Preserving Machine Learning Approach for Domain Shift Detection From Nonlinear Dynamic Responses of Structural Systems

Complex structural systems deployed for aerospace, civil, or mechanical applications must operate reliably under varying operational conditions. Structural health monitoring (SHM) systems help ensure the reliability of these systems by providing continuous monitoring of the state of the structure. SHM relies on synthesizing measured data with a predictive model to make informed decisions about structural states. However, these models—which may be thought of as a form of a digital twin—need to be updated continuously as structural changes (e.g., due to damage) arise. We propose an uncertainty-aware machine learning model that enforces distance preservation of the original input state space and then encodes a distance-aware mechanism via a Gaussian process (GP) kernel. The proposed approach leverages the spectral-normalized neural GP algorithm to combine the flexibility of neural networks with the advantages of GP, subjected to structure-preserving constraints, to produce an uncertainty-aware model. This model is used to detect domain shift due to structural changes that cannot be observed directly because they may be spatially isolated (e.g., inside a joint or localized damage). This work leverages detection theory to detect domain shift systematically given statistical features of the prediction variance produced by the model. The proposed approach is demonstrated on a nonlinear structure being subjected to damage conditions. In conclusion, it is shown that the proposed approach is able to rely on distances of the transformed input state space to predict increased variance in shifted domains while being robust to normative changes.

Algorithms↗

DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Landmark-Warped Emulators for Models with Misaligned Functional Response

Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Discovering the Unknowns: A First Step

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden changes in the data. We use Gaussian process modeling and a sparse representation of the sudden changes to efficiently estimate the large number of parameters in the proposed statistical model. The method is tested on a realistic dataset generated using a one-dimensional implementation of a Magnetized Liner Inertial Fusion (MagLIF) simulation model, and encouraging results are obtained.

42 ENGINEERING↗