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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Deployment of Multifidelity Uncertainty Quantification for Thermal Battery Assessment Part I: Algorithms and Single Cell Results

This report documents the results of an FY22 ASC V&V level 2 milestone demonstrating new algorithms for multifidelity uncertainty quantification. Part I of the report describes the algorithms, studies their performance on a simple model problem, and then deploys the methods to a thermal battery example from the open literature. Part II (restricted distribution) applies the multifidelity UQ methods to specific thermal batteries of interest to the NNSA/ASC program.

25 ENERGY STORAGE↗
DOE OSTI2020

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling-based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time-consuming if the simulation-based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. Finally, an algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Comparison of multifidelity machine learning models for potential energy surfaces

Multifidelity modeling is a technique for fusing the information from two or more datasets into one model. It is particularly advantageous when one dataset contains few accurate results and the other contains many less accurate results. Within the context of modeling potential energy surfaces, the low-fidelity dataset can be made up of a large number of inexpensive energy computations that provide adequate coverage of the N-dimensional space spanned by the molecular internal coordinates. The high-fidelity dataset can provide fewer but more accurate electronic energies for the molecule in question. Here, we compare the performance of several neural network-based approaches to multifidelity modeling. We show that the four methods (dual, Δ-learning, weight transfer, and Meng–Karniadakis neural networks) outperform a traditional implementation of a neural network, given the same amount of training data. We also show that the Δ-learning approach is the most practical and tends to provide the most accurate model.

Chemistry↗
DOE OSTI2023

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Furthermore, our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

42 ENGINEERING↗
DOE OSTI2022

Physics-informed CoKriging model of a redox flow battery

Vanadium redox flow batteries (VRFBs) offer the capability to store large amounts of energy cheaply and efficiently, however, there is a need for fast and accurate models of the charge–discharge curve of a VRFB to potentially improve the battery capacity and performance. Here, we develop a multifidelity model for predicting the charge–discharge curve of a VRFB. In the multifidelity model, we use the Physics-informed CoKriging (CoPhIK) machine learning method that is trained on experimental data and constrained by the so-called “zero-dimensional” physics-based model. Here we demonstrate that the model shows good agreement with experimental results and significant improvements over existing zero-dimensional models. We show that the proposed model is robust as it is not sensitive to the input parameters in the zero-dimensional model. We also show that only a small amount of high-fidelity experimental datasets are needed for accurate predictions for the range of considered input parameters, which include current density, flow rate, and initial concentrations.

25 ENERGY STORAGE↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Accelerated statistical failure analysis of multifidelity TRISO fuel models

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Quasi-Classical Trajectory Calculation of Rate Constants Using an Ab Initio Trained Machine Learning Model (aML-MD) with Multifidelity Data

Machine learning (ML) provides a great opportunity for the construction of models with improved accuracy in classical molecular dynamics (MD). However, the accuracy of a ML trained model is limited by the quality and quantity of the training data. Generating large sets of accurate ab initio training data can require significant computational resources. Furthermore, inconsistent or incompatible data with different accuracies obtained using different methods may lead to biased or unreliable ML models that do not accurately represent the underlying physics. Recently, transfer learning showed its potential for avoiding these problems as well as for improving the accuracy, efficiency, and generalization of ML models using multifidelity data. In this work, ab initio trained ML-based MD (aML-MD) models are developed through transfer learning using DFT and multireference data from multiple sources with varying accuracy within the Deep Potential MD framework. Further, the accuracy of the force field is demonstrated by calculating rate constants for the H + HO 2 → H 2 + 3 O 2 reaction using quasi-classical trajectories. We show that the aML-MD model with transfer learning can accurately predict the rate constants while reducing the computational cost by more than five times compared to the use of more expensive quantum chemistry training data sets. Hence, the aML-MD model with transfer learning shows great potential in using multifidelity data to reduce the computational cost involved in generating the training set for these potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parallel simulated annealing with embedded machine learning and multifidelity models for reactor core design

This paper presents extensions to a penalty-free, parallel simulated annealing (SA) algorithm for multi-constrained combinatorial optimization with the aim of embedding multi-fidelity physics models into the annealing procedure. The method uses a low-fidelity, quickly executing model for rapid design space exploration and a high-fidelity model for detailed constraint resolution and on-the-fly bias correction. Machine learning models updated within the annealing procedure were used to bridge the gap between the multi-fidelity models, which led to accurate rapid exploration and efficient detailed constraint resolution. A software implementation of the new multi-fidelity optimization methods, called ML-PSA, was demonstrated on a continuous multi-fidelity optimization problem and a constrained combinatorial PWR lattice design problem. These problems demonstrate some of the features, parallel performance characteristics, and extensible nature of the multi-fidelity SA methods. This paper shows that the developed software and procedure are a general optimization tool that can be applied to a wide variety of scientific and engineering design optimization applications. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. Here, the associated notebooks allow to reproduce the reported analyses and apply them to other systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗
DOE OSTI2026

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation) [SWR-26-095]

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation): Multifidelity aerodynamic polar data generation for hydrofoil/tidal-turbine airfoil sections. Foilpolars ties together three pieces: *AeroSandbox supplies the baseline airfoil coordinates (UIUC database). *G2Aero parameterizes those shapes on a Grassmannian manifold (Karcher mean + PGA basis) and samples new perturbed shapes around that basis. *XFoil (panel method) and NeuralFoil (neural-network surrogate, shipped with AeroSandbox) each solve the resulting shapes for lift, drag, moment, and pressure at the swept angles of attack, Reynolds numbers, and n_crit values. Design optimization of foil shapes in a computationally efficient way requires polars data across many candidate shapes, not just a handful of baseline foils. However, high-fidelity CFD at that scale is too costly, and naive shape perturbation strays from realistic geometries. FOILPOLARS addresses this by loading baseline airfoils (via AeroSandbox) and mapping them onto a Grassmannian manifold (via G2Aero), computing a Karcher mean and principal geodesic analysis (PGA) basis. New shapes are sampled by perturbing PGA coefficients, keeping them close to the manifold of realistic foils. Each sampled shape is evaluated across a configurable sweep of angle of attack, Reynolds number, and critical amplification factor using two solvers: XFoil (panel method) and NeuralFoil (neural-network surrogate), producing a paired dataset of lift, drag, moment, pressure, convergence, and confidence, indexed alongside each shape's PGA coefficients and shared Grassmannian basis in a single xarray dataset. From this, FOILPOLARS produces convergence summaries and comparison plots per shape, Reynolds number, and n_crit. A command-line interface exposes each pipeline stage independently, supporting data-driven design, optimization, and machine-learning workflows for foils.

Sandhu, Rimple [National Laboratory of the Rockies↗
DOE OSTI2025

Multifidelity_Timeseries

SAND2025-03305O Multifidelity Timeseries is a user-friendly tool designed to create advanced models for analyzing time-series data. It offers three modeling options, allowing users to choose the best fit for their specific needs. The software efficiently processes multiple data sources without the need for complex sampling methods. It helps uncover patterns and insights using data. The result is it is easier to make informed decisions for projects. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Katona, Ryan [Sandia National Lab. (SNL-CA), Liver↗
DOE OSTI2022

Active learning with multifidelity modeling for efficient rare event simulation

Here, while multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies (including some high-dimensional problems) and two finite element model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

42 ENGINEERING↗