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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Integrating adaptive learning with post hoc model explanation and symbolic regression to build interpretable surrogate models

Abstract We develop a materials informatics workflow to build an interpretable surrogate model for micromagnetic simulations. Our goal is to predict the energy barrier of a moving isolated skyrmion in rare-earth-free $$\hbox {Mn}_4$$ Mn 4 N. Our approach integrates adaptive learning with post hoc model explanation and symbolic regression methods. We discuss an unexplored acquisition function (information condensing active learning) within the adaptive learning loop and compare it with the known standard deviation function for efficient navigation of the search space. Model-agnostic post hoc explanation techniques then uncover trends learned by the trained model, which we then leverage to constrain the expressions used for symbolic regression. Graphical abstract

Biswas, Ankita↗
DOE OSTI2026

Surrogate model evaluation and building energy benchmarking for commercial buildings

Building energy consumption benchmarking involves challenges associated with various energy patterns for different building types; heating, ventilating, and air-conditioning (HVAC) system types; and climates. Given significant variation in energy use patterns, accurate prediction of long-term energy use using surrogate models remains challenging. Multiple linear regression (MLR) is commonly used for building energy benchmarking because of its simple structure; however, it lacks accuracy compared to other black-box models. Although many studies have compared surrogate models and offer guidance on model selection based on metrics, they do not provide detailed analysis on improving the surrogate model accuracy. In this paper, we implement a surrogate model using polynomial ridge regression (i.e., MLR with interaction terms combined with ridge regularization) for small office and retail strip mall buildings across six HVAC system types and all climate zones, for electricity and natural gas in baseline and proposed scenarios. A simulation workflow is developed using OpenStudio TM /EnergyPlus TM to generate simulation data using measures over a wide range of efficiency inputs. Enhancements based on statistical insights are used for improving the model accuracy using filters, input transformations, and change points. Surrogate models achieved average coefficient of variation of the root mean squared error (CVRMSE) values of 2.17, 1.06, 2.05, and 3.26 for proposed electricity, proposed natural gas, baseline electricity, and baseline natural gas, respectively, with enhancements reducing CVRMSE by an average of 14.9% across all combinations. We provide model interpretation via Shapley additive explanations to determine which input variables most influence energy consumption and provide supportive arguments for enhancements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2018

Probabilistic Sensitivity Analyses Incorporating Surrogate Models for the Structural Response of a Representative Inflatable Space Structure

This study concentrates on results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities and assess surrogate model suitability for a novel inflatable airlock concept, specifically the Non-Axisymmetric Inflatable Pressure Structure (NAIPS) under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. The current studies extended the demonstration of probabilistic analysis tools to identify parameter sensitivities by: incorporating nonlinear material load-strain property curves and orthotropic representation of the fabric; and exploring the use of surrogate models to facilitate rapid evaluations as new information becomes available, as well as enable optimizations. The airlock model has been simplified to focus on the end dome section. Brief overviews of the finite element model and associated surrogate models are provided along with the probabilistic sensitivity analysis approaches. Responses of interest include the sensitivities of various loads in the structural elements of the NAIPS to material properties, cord lengths, inflation pressure and friction between softgoods components. The use of surrogate models was explored to facilitate rapid sensitivity evaluations as parameter ranges change. The completion of the sensitivity studies improved understanding of the dependence of load responses to several uncertain parameters and confidence in the ability to use surrogate models to represent the finite element simulations.

Lyle, Karen H.↗
DOE OSTI2022

Quantifying subsurface parameter and transport uncertainty using surrogate modelling and environmental tracers

Here, we combine physics-based groundwater reactive transport modelling with machine-learning techniques to quantify hydrogeological model and solute transport predictive uncertainties. We train an artificial neural network (ANN) on a dataset of groundwater hydraulic heads and 3 H concentrations generated using a high-fidelity groundwater reactive transport model. Using the trained ANN as a surrogate model to reproduce the input–output response of the high-fidelity reactive transport model, we quantify the posterior distributions of hydrogeological parameters and hydraulic forcing conditions using Markov chain Monte Carlo calibration against field observations of groundwater hydraulic heads and 3 H concentrations. We demonstrate the methodology with a model application that predicts Chlorofluorocarbon-12 (CFC-12) solute transport at a contaminated field site in Wyoming, United States. Our results show that including 3 H observations in the calibration dataset reduced the uncertainty in the estimated permeability field and infiltration rates, compared to calibration against hydraulic heads alone. However, predictive uncertainty quantification shows that CFC-12 transport predictions conditioned to the parameter posterior distributions cannot reproduce the field measurements. We found that calibrating the model to hydraulic head and 3 H observations results in groundwater mean ages that are too large to explain the observed CFC-12 concentrations. The coupling of the physics-based reactive transport model with the machine-learning surrogate model allows us to efficiently quantify model parameter and predictive uncertainties, which is typically computationally intractable using reactive transport models alone.

58 GEOSCIENCES↗
DOE OSTI2025

Prototype-Wise Sensitivity Analysis of Urban Building Energy Simulation Surrogate Modeling Accuracy

Urban Building Energy Modeling (UBEM) is an important reference for urban energy-related policymaking. Because of the significant impact of urban microclimates on the energy simulation, UBEM requires simulations of many microclimate-prototype pairs. Surrogate modeling is commonly used to reduce the cost of simulation computations. In UBEM surrogate modeling, it is important to determine the percentage of microclimates related to a prototype used for generating surrogate model training data. This study analyzes the prototype-wise variations and sensitivities of surrogate model estimation accuracy to the microclimate sampling ratios. The results of the study can help determine the number of simulations used for generating surrogate modeling data, avoid redundant simulations, and reduce the computational cost for UBEM surrogate modeling and its time.

Pan, Xiyu↗
DOE OSTI2025

Selection of Sampling and Surrogate Modeling Methods for State-Point Evaluations of an AGN-201M Reactor

Nuclear reactor digital twins (DTs) have been proposed for use as a safeguards technology to efficiently monitor new and novel reactors as they come online. A safeguards DT needs to be capable of detecting misuse and diversion as they occur, requiring physics models to be accurate and efficient. Mathematical surrogate models are capable of achieving the necessary efficiency and can largely maintain the accuracy of higher-order models given a quality training sample. The Multiphysics Object-Oriented Simulation Environment (MOOSE) code framework is specifically equipped to generate training samples and create surrogate models using full-order reactor physics models. Utilizing an operational AGN-201M reactor’s specifications, two surrogate types were trained on samples of variable size, and using Cartesian products, Latin hypercube sampling, and quadrature sampling, each was compared and evaluated on accuracy when compared to a full-order Monte Carlo model. Both surrogate types were able to capture reactivity changes within 0.05 $ of the Monte Carlo model while reducing the computation costs by eight orders of magnitude.

MOOSE↗
NASA NTRS2017

Program to Optimize Simulated Trajectories II (POST2) Surrogate Models for Mars Ascent Vehicle (MAV) Performance Assessment

The primary purpose of the multiPOST tool is to enable the execution of much larger sets of vehicle cases to allow for broader trade space exploration. However, this exploration is not achieved solely with the increased case throughput. The multiPOST tool is applied to carry out a Design of Experiments (DOE), which is a set of cases that have been structured to capture a maximum amount of information about the design space with minimal computational effort. The results of the DOE are then used to fit a surrogate model, ultimately enabling parametric design space exploration. The approach used for the MAV study includes both DOE and surrogate modeling. First, the primary design considerations for the vehicle were used to develop the variables and ranges for the multiPOST DOE. The final set of DOE variables were carefully selected in order to capture the desired vehicle trades and take into account any special considerations for surrogate modeling. Next, the DOE sets were executed through multiPOST. Following successful completion of the DOE cases, a manual verification trial was performed. The trial involved randomly selecting cases from the DOE set and running them by hand. The results from the human analyst's run and multiPOST were then compared to ensure that the automated runs were being executed properly. Completion of the verification trials was then followed by surrogate model fitting. After fits to the multiPOST data were successfully created, the surrogate models were used as a stand-in for POST2 to carry out the desired MAV trades. Using the surrogate models in lieu of POST2 allowed for visualization of vehicle sensitivities to the input variables as well as rapid evaluation of vehicle performance. Although the models introduce some error into the output of the trade study, they were very effective at identifying areas of interest within the trade space for further refinement by human analysts. The next section will cover all of the ground rules and assumptions associated with DOE setup and multiPOST execution. Section 3.1 gives the final DOE variables and ranges, while section 3.2 addresses the POST2 specific assumptions. The results of the verification trials are given in section 4. Section 5 gives the surrogate model fitting results, including the goodness-of-fit metrics for each fit. Finally, the MAV specific results are discussed in section 6.

Zwack, M. R.↗
DOE OSTI2022

A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models

This work presents the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for treatment of crud deposition as a constraint within light-water reactor core loading pattern optimization. The neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated. Analysis found that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence is presented that shows boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the methods employed provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Higher-order factorization machine for accurate surrogate modeling in material design

Efficient and robust optimization is important in material science for identifying optimal structural parameters and enhancing material performance. Surrogate-based active learning algorithms have recently gained great attention for their ability to efficiently navigate large, high-dimensional design spaces. Among surrogate models, 2 nd -order factorization machine (FM) models are widely employed as the surrogate model in active learning algorithms due to their balance between simplicity and effectiveness. However, their quadratic nature limits their capacity to capture complex, higher-order interactions among variables, often leading to suboptimal solutions. To overcome this limitation, we propose an active learning scheme integrating a 3 rd -order FM model, capable of modeling three-variable interactions and more intricate relationships in material systems. We comprehensively evaluate the surrogate modeling performance of the 3 rd -order FM case using various objective functions. Furthermore, we examine the optimization reliability and efficiency of the 3 rd -order FM-based active learning in a real-world material design task (e.g., nanophotonic structures for transparent radiative cooling). Our study shows that the 3 rd -order FM outperforms the 2 nd -order model in both surrogate accuracy and optimization performance, highlighting higher-order models’ promises for material design and optimization problems.

Factorization machine↗
DOE OSTI2024

Surrogate modelling for urban building energy simulation based on the bidirectional long short-term memory model

Here, the urban microclimate is essential for accurate simulation-based urban building energy modelling (UBEM). However, a high spatial-resolution microclimate can increase the computational resources demands of UBEM. Surrogate modelling is one of the promising approaches for fast UBEM. This study proposes a bidirectional Long Short-Term Memory (LSTM)-based approach for simulation-based UBEM surrogate modelling. The estimations are aggregated into census tracts using total building floor area. A case study using UBEM to estimate annual hourly building energy use and anthropogenic heat from all existing buildings in Los Angeles County found that most of the surrogate models can complete the annual hourly simulation within 90 minutes with a normalized mean absolute error lower than 10%, and that the bidirectional LSTM outperforms the standard LSTM in accuracy. This study demonstrates the advantages of bidirectional RNN architecture in building energy surrogate modelling and is expected to promote long-term and high-resolution UBEM with detailed microclimates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2011

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

A surrogate model methodology is described for predicting, during flight, the residual strength of aircraft structures that sustain discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. Two ductile fracture simulations are presented to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data does, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Spear, Ashley D.↗
NASA NTRS2011

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

A surrogate model methodology is described for predicting in real time the residual strength of flight structures with discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. A residual strength test of a metallic, integrally-stiffened panel is simulated to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data would, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high-fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Spear, Ashley D.↗
DOE OSTI2024

Advanced surrogate model for electron-scale turbulence in tokamak pedestals

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor q, electron beta β e and normalized electron Debye length λ D , in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport.

fusion plasma↗
DOE OSTI2024

Calibration of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation with Machine Learning Surrogate Models

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory is one of the most powerful accelerator-driven neutron sources in the world. The intense protons strike on SNS's mercury target to provide bright neutron beams, which also leads to severe fluid-structure interactions inside the target. Prediction of resultant loading on the target is difficult particularly when helium gas is injected into mercury to reduce the loading and mitigate the pitting damage on vessel walls. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this multi-physics problem. However, several uncertain parameters in the R-P model require intensive simulations to determine their optimal values. With the help of machine learning and the measured target strain, we have studied the major uncertain parameters in this R-P model and developed a framework to identify optimal parameters that significantly reduce the discrepancy between simulations and experimental strains. The preliminary results show the possibility of using this mercury/helium mixture and surrogate models to predict a better match of target strain response when the helium gas is injected.

Lin, Lianshan↗
DOE OSTI2025

Forecasting Multi-Step-Ahead Street-Scale Nuisance Flooding using a seq2seq LSTM Surrogate Model for Real-Time Application in a Coastal-Urban City

In coastal-urban cities facing an elevated risk of nuisance flooding (by rain and tide) due to increased heavy rainfall, sea level rise, urbanization, and aging drainage systems, real-time flood forecasting at the street-scale can provide useful information to transportation decision-makers. Physics-Based Models (PBMs) that offer high accuracy come with high computational runtimes and costs that limit their application for real-time flood forecasting. To address this challenge, Machine Learning (ML) surrogate models trained from PBMs have been proposed to provide street-scale flood forecasts. Previous related studies have focused on using Long Short-Term Memory (LSTM) architectures to model hourly flood depth on streets. While LSTM models can capture input sequences effectively, they fall short in accurately preserving output sequences, limiting their suitability for multi-step-ahead forecasts. The seq2seq LSTM architecture offers a key advantage here by capturing the full sequence of input–output, making it potentially more suitable for multi-step-ahead flood forecasts compared to traditional LSTM models. However, seq2seq LSTM has not been tested for street-scale flood forecasting, particularly for rapidly fluctuating nuisance flooding events which require special attention to its temporal sequences. Hence, in this study, we applied the seq2seq LSTM model to explore multi-step-ahead street-scale nuisance flooding and compared its results to the traditional LSTM model as a benchmark model. LSTM and seq2seq LSTM surrogate models were applied to 22 flood-prone streets in Norfolk, Virginia, as a case study with a 4-hr (short-term) and 8-hr (long-term) lead time. The models were trained with environmental (rainfall and tide) and topographic (elevation, Topographic Wetness Index, and Depth-To-Water) features along with PBM-derived water depths for different storm events. The results demonstrated satisfactory performance of both LSTM and seq2seq LSTM surrogate models throughout the forecast period compared to the PBM. However, the seq2seq LSTM showed lower Mean Absolute Error (MAE)/ Root Mean Square Error (RMSE) and higher Nash–Sutcliffe Efficiency (NSE)/ correlation than the LSTM across most lead times, particularly for long-term forecasting due to its supremacy in handling both input–output sequences together, which is missing in the traditional LSTM. For example, in the long-term, the average RMSE ranges were 0.0268–0.0373 m for LSTM and 0.0226–0.0319 m for seq2seq LSTM, while in the short-term, they were 0.0263–0.0293 m and 0.0261–0.0283 m, respectively. Additionally, while both models exhibited similar performance in distinguishing flooded and non-flooded streets for flood depth ≥ 0.1 m, the seq2seq LSTM model demonstrated superior performance for higher flood depths (such as ≥ 0.2 m and ≥ 0.3 m). Once trained, inference took only 0.09 to 0.11 s (short-term) and 0.30 to 0.35 s (long-term) per storm event for the 22 streets, making the application highly suitable for real-time decision-making during nuisance flood events.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Self-consistent equilibrium and transport simulations for NSTX-U plasmas enhanced via machine learning surrogate models

The Control-Oriented Transport SIMulator (COTSIM) is an advanced equilibrium and transport code designed for simulating tokamak discharges at computational speeds suitable for control applications. COTSIM’s modular framework enables users to select models that balance accuracy with speed according to specific needs, allowing the code to operate from fast to faster-than-real-time performance levels. This work presents recent enhancements to COTSIM’s predictive accuracy for NSTX-U scenarios, achieved by integrating neural-network-based surrogate models and self-consistent equilibrium calculations. To improve source deposition predictions, a surrogate model for NUBEAM has been incorporated. Additionally, a surrogate model for the Multi-Mode Module (MMM) now supports predictions of anomalous thermal, momentum, and particle diffusivities—key factors for modeling the evolution of temperature and rotation. Each surrogate model was specifically trained for the NSTX-U operational regime to enhance COTSIM’s accuracy while maintaining computational efficiency. Moreover, COTSIM now couples fixed-boundary equilibrium solvers with its transport solvers, enabling self-consistent predictions of plasma profiles and equilibrium evolution over the discharge. Simulation results demonstrate strong agreement between COTSIM and TRANSP predictions for NSTX-U discharges. These substantial advancements expand COTSIM’s utility in model-based control applications for NSTX-U. Potential applications include simultaneous optimization of equilibrium and transport scenarios, integration into digital twins, real-time profile estimation (e.g., temperature and rotation) from limited or noisy measurements, and advanced feedback-based scenario control.

Equilibrium and transport modeling↗
DOE OSTI2024

Surrogate Model Guided Optimization of Expensive Black-Box Multi-Objective Problems: A Posteriori Methods

Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.

MATHEMATICS AND COMPUTING↗
DOE OSTI2025

HOLISTIC CREDIBILITY ASSESSMENT OF A MACHINE LEARNING-BASED SURROGATE MODEL IN AN AERODYNAMICS APPLICATION

Elements of ASME V&V 20 credibility assessment methodology are used in tandem with credibility assessment tools from the machine learning community to assess the credibility of a deep neural network based surrogate model. This surrogate model is trained, tested, validated, and employed in the context of aerodynamic coefficient prediction for a NACA 0012 airfoil in subsonic and transonic flow. The parameter space is defined by angle of attack, Reynolds number, and Mach number.

Kirsch, Jared Roelof [Sandia National Laboratories↗