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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Simulation and Flight Test Capability for Testing Prototype Sense and Avoid System Elements

NASA Langley Research Center (LaRC) and The MITRE Corporation (MITRE) have developed, and successfully demonstrated, an integrated simulation-to-flight capability for evaluating sense and avoid (SAA) system elements. This integrated capability consists of a MITRE developed fast-time computer simulation for evaluating SAA algorithms, and a NASA LaRC surrogate unmanned aircraft system (UAS) equipped to support hardware and software in-the-loop evaluation of SAA system elements (e.g., algorithms, sensors, architecture, communications, autonomous systems), concepts, and procedures. The fast-time computer simulation subjects algorithms to simulated flight encounters/ conditions and generates a fitness report that records strengths, weaknesses, and overall performance. Reviewed algorithms (and their fitness report) are then transferred to NASA LaRC where additional (joint) airworthiness evaluations are performed on the candidate SAA system-element configurations, concepts, and/or procedures of interest; software and hardware components are integrated into the Surrogate UAS research systems; and flight safety and mission planning activities are completed. Onboard the Surrogate UAS, candidate SAA system element configurations, concepts, and/or procedures are subjected to flight evaluations and in-flight performance is monitored. The Surrogate UAS, which can be controlled remotely via generic Ground Station uplink or automatically via onboard systems, operates with a NASA Safety Pilot/Pilot in Command onboard to permit safe operations in mixed airspace with manned aircraft. An end-to-end demonstration of a typical application of the capability was performed in non-exclusionary airspace in October 2011; additional research, development, flight testing, and evaluation efforts using this integrated capability are planned throughout fiscal year 2012 and 2013.

Howell, Charles T.↗
NASA NTRS2017

Passive Earth Entry Vehicle Landing Test

Two full-scale passive Earth Entry Vehicles (EEV) with realistic structure, surrogate sample container, and surrogate Thermal Protection System (TPS) were built at NASA Langley Research Center (LaRC) and tested at the Utah Test and Training Range (UTTR). The main test objective was to demonstrate structural integrity and investigate possible impact response deviations of the realistic vehicle as compared to rigid penetrometer responses. With the exception of the surrogate TPS and minor structural differences in the back shell construction, the two test vehicles were identical in geometry and both utilized the Integrated Composite Stiffener Structure (ICoSS) structural concept in the forward shell. The ICoSS concept is a lightweight and highly adaptable composite concept developed at NASA LaRC specifically for entry vehicle TPS carrier structures. The instrumented test vehicles were released from a helicopter approximately 400 m above ground. The drop height was selected such that at least 98% of the vehicles terminal velocity would be achieved. While drop tests of spherical penetrometers and a low fidelity aerodynamic EEV model were conducted at UTTR in 1998 and 2000, this was the first time a passive EEV with flight-like structure, surrogate TPS, and sample container was tested at UTTR for the purpose of complete structural system validation. Test results showed that at a landing vertical speed of approximately 30 m/s, the test vehicle maintained structural integrity and enough rigidity to penetrate the sandy clay surface thus attenuating the landing load, as measured at the vehicle CG, to less than 600 g. This measured deceleration was found to be in family with rigid penetrometer test data from the 1998 and 2000 test campaigns. Design implications of vehicle structure/soil interaction with respect to sample container and sample survivability are briefly discussed.

Kellas, Sotiris↗
NASA NTRSDate not supplied

Probabilistic Modeling of a Three-Stage Human Landing System Architecture

Space Policy Directive-1 has led to NASA partnerships with commercial entities on procurement which includes the development of the Human Landing System (HLS) [1]. With the goal of delivering human crew to the lunar surface by 2024, system uncertainties become an important obstacle to the maturation of multiple new, driving technologies and mission concepts of the HLS program. As unmitigated uncertainties have previously led to failed development programs, these risks and their impacts must be understood and handled to ensure program success [2]. Sources of uncertainty include novel engine designs and configurations, increased reliance on cryogenic fluid management(CFM), and refueling technologies—which propagate as high-level performance metrics such as overall propellant mass and engine performance. Also, the occurrence of operational uncertainties—e.g. launch conditions or need to abort during the mission—can cause cascading effects on the rest of the mission that are difficult to definitively quantify, and are outside the scope of control. These concrete examples and other occurrences can be categorized as either epistemic or aleatory uncertainties.Epistemic uncertainty arises due to a lack of knowledge and can be alleviated with design and program maturation. Aleatory uncertainty is due to the inherent randomness of the system and cannot be directly reduced, unlike epistemic uncertainty. Robust design and probabilistic methods can compensate for aleatory effects. A taxonomy of uncertainty is referred to for this work [3]. In this paper, a probabilistic methodology to handle uncertainties has been demonstrated on a three-element HLS concept [1, 4], which allows tracking of current best estimates of the concept and assessment of concept design robustness against uncertainties. A sample case has been completed for this abstract, and an expansion on the methodology will be included in the final paper. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. This abstract will cover the basics of the approach used, and further details and justifications will be in the final paper.The mission profile associated with this three-element concept (Fig 1) was modeled as a set of mission events that facilitated mass changes, idles, or spacecraft maneuvers. The mission profile scope starts with each element’s NRHO orbit insertion and aggregation and ends at post-sortie rendezvous with Orion. More detail on the mission profile will be in the final paper. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as the physics framework to model the HLS architecture for applying the probabilistic methodology [5, 6]. Specifically, a parametric representation of the lander, ascent, and transfer elements and the mission profile of each element was established, with vehicle and mission parameters available as inputs to allow for a dynamic model. Each vehicle stage was modeled with high-level performance metrics, using Isp and propellant mass fraction (PMF) to remain parametric. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. These parameters were frozen at their nominal values for the purposes of baselining architecture performance and sizing the vehicle appropriately based on reference documentation [1]. Range estimating—a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities—is traditionally used with Mass Equipment Lists (MELs), but has been adapted with operational parameters as well as vehicle parameters in theDYREQT model to capture mission uncertainty alongside vehicle uncertainty [7, 3]. This method was selected due to its application and insight on a system from a bottom-up perspective, independence from historical rules of thumb, and ability to generate sensitivities based on design decisions and uncertainties. As a sample case for the abstract, the boiloff rates of the vehicle elements and the loiter times during the mission (simulating launch time variations and changing window of opportunities) were used with range estimating to provide preliminary results. To perform the range estimation portion of this methodology (depicted in Fig. 3, further details in final paper), the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the sample set of uncertainty parameters; 5,000 cases via Latin Hypercube Sampling were computed on the DYREQT architecture model. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Range estimating was applied to the surrogates instead of the actual models, which saves computational expense due to the bulk of cases needed for the Monte Carlo simulation as part of range estimating. Uncertainty parameters were sampled independently from triangular distributions using the DoE ranges as ‘min’ and ‘max’, and the nominal value as ‘most likely’. Based engineering intuition, some uncertainty parameters are correlated—e.g. if the main propellant has a high boil-off rate, the oxidizer should follow suit as both are related to CFM technology.While a Monte Carlo simulation samples all inputs as independent, the results would show model correlations; thus, it is efficient to sample the inputs as correlated. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo. A table for the DoE ranges and probability distribution parameters is shown in Table 1, and more details on Correlated Monte Carlo Simulations will be discussed in the final paper. The model’s resulting DoE showed that multivariate polynomial equations fit via least squares method captured its behavior accurately for the sample case. For the Correlated Monte Carlo Simulation, a positive correlation between fuel and oxidizer boiloff rates was used as a demonstration. 10,000 cases were computed with the surrogates and the launched masses for each vehicle element was collated. The results can be displayed in a probability density function (PDF), showing the impact of the uncertainty parameters chosen. Integrating the PDFs will yield a cumulative distribution function (CDF) that shows the cumulative probability of a given value on the x-axis. For the sample case, the elements’ launch mass margin was calculated and represented in as CDFs, as a demonstrated representation of figures of merit for the HLS concept. For the lander and ascent elements, the NRHO mass insertion limit is 16t; the transfer element has a limit of 30t [1]. It can be seen with Figure 2 that this probabilistic methodology can provide insight into mass margin with respect to the uncertainties being modeled. Currently, the results show that the lander (descent) vehicle element has the most restrictive design space; it is the only element to show a 10% probability of negative margin. Further analysis on the Monte Carlo results will show sensitivities for driving constraints and parameters for architecture feasibility, which can lead to establishing potential mission rules.The combination of range estimating with a parametric architecture model for HLS demonstrated the capability of this probabilistic methodology in a sample case. As the HLS development progresses, this methodology has the potential for keeping current best estimates of architecture performance for awarded concepts due to the flexibility in DYREQT’s modeling framework and its parametric nature. Concept maturation and increased epistemic knowledge can be injected into the model probabilistic modeling, and thus continue to track probability of mission success.

Stephanie Y Zhu↗
NASA NTRS2022

A Robust Machine Learning Schema for Developing, Maintaining, and Disseminating Machine Learning Models

Recent advances in the development of machine learning (ML) algorithms have enabled the creation of predictive models that can improve decision making, decrease computational cost, and improve efficiency in a variety of fields. As an organization begins to develop and implement such models, the data used in the training, validation, and testing of ML models, the model parameters, and the use cases or limitations of the models must be properly stored to ensure models are both fully traceable and used correctly. In the context of predicting material behavior, advances in computationally intense, physics-based modeling of material behavior at various length scales and the emergence of Integrated Computational Materials Engineering (ICME) have driven the need for developing data-driven surrogate models of the physics-based simulation tools using ML techniques. Surrogate model development allows for accurate material behavior prediction at a fraction of the cost of its physics-based counterpart, allowing for multiscale simulations of real-world applications, further enabling the ability to design fit-for-purpose materials for a reasonable computational investment. However, training such models requires extensive data, and thus, effective data management is necessary to reach the full potential that ML can offer to material design and ICME. This paper proposes a generalized, robust schema that allows organizations to store both real (experimental) and virtual (simulation) data used to train ML models and the defining model parameters and architectures within the Granta MI Platform. The developed schema allows for various types of data inputs and outputs, including single point values, time-series data, and images that can be used in the prediction of material behavior, while following outlined best practices for effective data management. An effective schema for ML data and models can help prevent the recreation of virtual/real training data and surrogate models, help reduce the time to create new models similar to existing ones by offering a starting point in the hyperparameter determination stages, minimize resources devoted to verification and validation (V&V) and certification of models, and ensure that data and surrogate models are not misused due to full traceability of both the data and ML model. It also allows organizations access to models that have already been developed, such that they can be used in the design of new materials, enabling the overall goals of ICME.

Brandon L. Hearley↗
NASA NTRSDate not supplied

Predicting Fiber Failure of Plain Weave Fabric with Recursive Multiscale Micromechanics

Recent advances in the development of machine learning (ML) algorithms have enabled the creation of predictive models that can improve decision making, decrease computational cost, and improve efficiency in a variety of fields. As an organization begins to develop and implement such models, the data used in the training, validation, and testing of machine learning models, the model parameters, and the use cases or limitations of the models must be properly stored to ensure models are both fully traceable and used correctly. In the context of predicting material behavior, advances in computationally intense, physics-based, modeling of material behavior at various length scales, and the emergence of Integrated Computational Materials Engineering (ICME) have driven the need for developing data-driven surrogate models of the physics-based simulation tools using machine learning (ML) techniques. Surrogate model development allows for accurate material behavior prediction at a fraction of the cost of its physics-based counterpart, allowing for multiscale simulations of real-world applications, further enabling the ability to design fit-for-purpose materials for a reasonable computational investment. However, training such models requires extensive data, and thus effective data management is necessary to reach the full potential that ML can offer to material design and ICME. This paper proposes a generalized, robust schema that allows organizations to store both real (experimental) and virtual (simulation) data used to train machine learning models and the defining model parameters and architectures. The developed schema allows for various types of data inputs and outputs, including single point values, time-series data, and images that can be used in for various types of machine learning models while following outlined best practices for effective data management. An effective schema for machine learning data and models can help prevent the recreation of virtual/real training data and surrogate models, can help reduce the time to create new models similar to existing ones by offering a starting point in the hyperparameter determination stages, minimize resources devoted to verification and validation (V&V) and certification of models, and ensure that data and surrogate models are not misused due to full traceability of both the data and ML model. It also allows organizations access to models that have already been developed, such that they can be used in the design of new materials, enabling the overall goals of ICME.

Failure↗
NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗
NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Principal Component Analysis↗
NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Computational Fluid Dynamics↗
DOE OSTI2022

Computational Workflow for Accelerated Molecular Design Using Quantum Chemical Simulations and Deep Learning Models

Efficient methods for searching the chemical space of molecular compounds are needed to automate and accelerate the design of new functional molecules such as pharmaceuticals. Given the high cost in both resources and time for experimental efforts, computational approaches play a key role in guiding the selection of promising molecules for further investigation. Here, we construct a workflow to accelerate design by combining approximate quantum chemical methods [i.e. density-functional tight-binding (DFTB)], a graph convolutional neural network (GCNN) surrogate model for chemical property prediction, and a masked language model (MLM) for molecule generation. Property data from the DFTB calculations are used to train the surrogate model; the surrogate model is used to score candidates generated by the MLM. The surrogate reduces computation time by orders of magnitude compared to the DFTB calculations, enabling an increased search of chemical space. Furthermore, the MLM generates a diverse set of chemical modifications based on pre-training from a large compound library. We utilize the workflow to search for near-infrared photoactive molecules by minimizing the predicted HOMO-LUMO gap as the target property. Our results show that the workflow can generate optimized molecules outside of the original training set, which suggests that iterations of the workflow could be useful for searching vast chemical spaces in a wide range of design problems.

Blanchard, Andrew↗
DOE OSTI2023

Adaptive Data-Driven Model Predictive Control for Heat Pipe Microreactors

To establish a technical basis for self-regulating microreactors, a model predictive control (MPC) system is investigated to proactively respond to anomalies and disturbances in anticipation of potential deviations from operating setpoints. Due to the difficulty of developing a physics-based surrogate model that can accurately match plant data in various operating conditions, machine learning algorithms are used in MPC, which allow for learning from both simulation and operation data, thus efficiently describing the targeted transient with arbitrary accuracy. However, one of the biggest concerns in applying ML algorithms like artificial neural networks (ANNs) is that the predictive capabilities of ANN are limited by training data. If there are gaps between the training and target domain, the accuracy of an ANN can degrade significantly when it is used to predict unseen data. To improve the predictive capability of ANN and enable a confident use of data-driven MPCs outside the training data, this study proposes an adaptive data-driven MPC framework. The system will monitor the discrepancy between plant responses and surrogate predictions, fine-tune the ANN-based surrogate when a large discrepancy is detected, and continue MPC operation with updated surrogates. The framework is demonstrated on a point kinetic model for microreactors. The hyperparameters of the update strategy, including layers to update, error thresholds, learning rate discount, and number of data points used for fine-tuning, are optimized so the simulated microreactor is able to follow changes in setpoint with the smallest of deviations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Adaptable Data Driven Model Predictive Control for Heat Pipe Microreactors

To establish a technical basis for self-regulating microreactors, a model predictive control (MPC) system is investigated to proactively respond to anomalies and disturbances in anticipation of potential deviations from operating setpoints. Due to the difficulty of developing a physics-based surrogate model that can accurately match plant data in various operating conditions, machine learning algorithms are used in MPC, which allow for learning from both simulation and operation data, thus efficiently describing the targeted transient with arbitrary accuracy. However, one of the biggest concerns in applying ML algorithms like artificial neural networks (ANNs) is that the predictive capabilities of ANN are limited by training data. If there are gaps between the training and target domain, the accuracy of an ANN can degrade significantly when it is used to predict unseen data. To improve the predictive capability of ANN and enable a confident use of data-driven MPCs outside the training data, this study proposes an adaptive data-driven MPC framework. The system will monitor the discrepancy between plant responses and surrogate predictions, fine-tune the ANN-based surrogate when a large discrepancy is detected, and continue MPC operation with updated surrogates. The framework is demonstrated on a point kinetic model for microreactors. The hyperparameters of the update strategy, including layers to update, error thresholds, learning rate discount, and number of data points used for fine-tuning, are optimized so the simulated microreactor is able to follow changes in setpoint with the smallest of deviations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Rapid Inverse Parameter Inference Using Physics-Informed Neural Network

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration. However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model. Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs.

Bayesian calibration↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Cerium oxide impact on fresh and hardened properties of cementitious materials

Cements used in global nuclear waste treatment, storage, and disposal require thorough testing of fresh and cured properties to demonstrate regulatory compliance. Using actual radioactive wastes is often cost-prohibitive during early scoping tests necessitating the use of non-radiological surrogates. Cerium (Ce) is often used as a surrogate for actinides uranium (U) and plutonium (Pu) in spent nuclear fuel, yet few studies have explored how Ce impacts the properties used to qualify a cement for use. Here, this work compares the fresh and cured properties of three classes of cements – ordinary portland cements, ultra-high performance cement composites, and magnesium phosphate cements – each with and without ceria (CeO 2 ). Due to CeO 2 sorption of water (54 vol%) that effectively decreases the water available to hydrate and form binding cement phases, variations in key cement properties were detected that suggest surrogate CeO 2 –cementitious matrices may not be representative of matrix behaviors when using U and Pu sources.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning↗
DOE OSTI2022

Dispersion-enhanced sequential batch sampling for adaptive contour estimation

In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
DOE OSTI2025

Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from the NRHybSur3dq8 surrogate, which provides spherical-harmonic modes up to $\ell$ ≤ 4 (excluding (4, 0) and (4,±1), and including (5, 5)) for mass ratios q ≤ 8, dimensionless spin components s$^{z}_{1,2}$ ϵ[–0.8, 0.8], and inclination angles θ ϵ [0, π]. Waveforms are supplied on the interval t ϵ [–5000M, –100 M) and the model autoregressively generates the plus and cross polarizations (h + , h x ) on t ϵ [–100 M, 130M]. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required ~15 h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of 840,000 samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth.

black-hole merger↗