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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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At least 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Uncertainty propagation in feed-forward neural network models

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

MLP networks↗
DOE OSTI2020

Evaluating 239 Pu(n,f) cross sections via machine learning using experimental data, covariances, and measurement features

In this paper, the neutron-induced 239 Pu fission cross section, 239 Pu(n,f), is evaluated from 1–20 MeV using experimental data and associated covariances while also considering information on the measurement, termed features here. For instance, methods to determine the background, sample backing material, or impurities in the sample, are explicitly taken into account in the evaluation process. To this end, outliers in the experimental data are identified with a modified version of the Hybrid Robust Support Vector Machine. In a second step, two machine learning methods (logistic regression with elastic net regularization and random forest regression with SHAP feature importance metric) are used to highlight measurement features that are common among many of the outlying data points. Based on this analysis, penalty uncertainties are added to the experimental covariances of outlying data points that have outlier measurement features and are put through the generalized-least-squares evaluation. The resulting evaluated mean values and covariances differ distinctly from those data evaluated without the penalty uncertainties. These results highlight that certain measurement features should be more closely examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

An investigation on machine learning predictive accuracy improvement and uncertainty reduction using VAE-based data augmentation

The confluence of ultrafast computers with large memory, rapid progress in Machine Learning (ML) algorithms, and the availability of large datasets place multiple engineering fields at the threshold of dramatic progress. However, a unique challenge in nuclear engineering is data scarcity because experimentation on nuclear systems is usually more expensive and time-consuming than most other disciplines. One potential way to resolve the data scarcity issue is deep generative learning, which uses certain ML models to learn the underlying distribution of existing data and generate synthetic samples that resemble the real data. In this way, one can significantly expand the dataset to train more accurate predictive ML models. In this study, our objective is to evaluate the effectiveness of data augmentation using variational autoencoder (VAE)-based deep generative models. We investigated whether the data augmentation leads to improved accuracy in the predictions of a deep neural network (DNN) model trained using the augmented data. Additionally, the DNN prediction uncertainties are quantified using Bayesian Neural Networks (BNN) and conformal prediction (CP) to assess the impact on predictive uncertainty reduction. To test the proposed methodology, we used TRACE simulations of steady-state void fraction data based on the NUPEC Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. Here, we found that augmenting the training dataset using VAEs has improved the DNN model’s predictive accuracy, improved the prediction confidence intervals, and reduced the prediction uncertainties.

Bayesian neural network↗
DOE OSTI2021

A probability density function model describing height estimation uncertainty due to image pixel intensity noise in digital fringe projection measurements

Digital fringe projection is a surface-profiling technique used for highly accurate non-contact measurements. As with any measurement technique, a variety of sources degrade to the measurement accuracy of the method. Here, this paper presents an analytically-derived probability density function that explicitly models the surface height measurement error due to inevitable phase measurement error, and it includes the specific case of pixel noise inducing the phase measurement error that ultimately leads to the height estimation error. The accuracy of the model was validated through Monte-Carlo simulations of resultant height distributions subject to arbitrarily correlated pixel intensity noise and experimental digital fringe projection measurements where the pixel-by-pixel height uncertainty estimations were compared to the predictions of the derived model.

42 ENGINEERING↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2026

Decoding the proton’s gluonic density with lattice QCD-informed machine learning

We present a first machine learning-based decoding of the gluonic structure of the proton from lattice QCD using a variational autoencoder inverse mapper (VAIM). Harnessing the power of generative AI, we predict the parton distribution function (PDF) of the gluon given information on the reduced pseudo-Ioffe-time distributions (RpITDs) as calculated from an ensemble with lattice spacing a ≈ 0.09 fm and a pion mass of M π ≈ 310 MeV. The resulting gluon PDF is consistent with phenomenological global fits within uncertainties, particularly in the intermediate-to-high-x region where lattice data are most constraining. A subsequent correlation analysis confirms that the VAIM learns a meaningful latent representation, highlighting the potential of generative AI to bridge lattice QCD and phenomenological extractions within a unified analysis framework.

Gluon parton distribution function↗
DOE OSTI2022

Analysis of historic fires to determine most frequent challenging events

The fire probabilistic risk assessment framework for nuclear power plants relies on experimental data to determine expected fire behavior or to validate models to predict fire conditions in the plant. To support reducing the uncertainty in this experimental data, a research effort was conducted to identify the most frequent and challenging fire scenarios using historic fire data from nuclear power plants in the United States. To support this effort, an electronic version of the publicly available Updated Fire Event Database developed by Electric Power Research Institute was produced resulting in data on 2111 fire events, 540 events were labelled as being challenging fires with 74.2% of these challenging fire events being due to eleven selected fire types. In conclusion, of these fire types, electrical and electronic equipment, transient combustibles, and liquid fires were the most frequent of the challenging fires. The fire scenario specifics were characterized for each of the eleven selected types and then related to existing fire experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Systematic exploration of the thermochemistry for a set of peroxy hydroperoxy-alkyl radicals

Here, the thermochemistry of peroxy hydroperoxy-alkyl ($\overline{O}$OQOOH) radicals has a significant influence on the reactivity of fuels and on the formation of highly oxygenated molecules (HOMs) in the atmosphere. Theoretical characterization of these radicals can be arduous due to their molecular size and complex fundamental interactions, such as hydrogen-bonding and torsional anharmonicity, and difficult to validate in the absence of any direct experimental thermochemical data. In this work, we systematically explore the thermochemistry of a set of $\overline{O}$OQOOH radicals with five increasingly affordable approaches with considerations for these interactions. In doing so, we present a novel conformer selection approach suited to predict properties at combustion temperatures. As a corollary, we also highlight the shortcomings in the standard choice of the ground conformer as the reference. The set of molecules is comprised of 149 C 2 -C 8 $\overline{O}$OQOOH radicals, selected to encompass a wide variety of branching and substitution patterns. Comparisons amongst the approaches help quantify the errors arising from various simplifying assumptions. For the largest of these radicals, and with the most affordable approach, final predictions of Gibbs energies are assigned a 2 σ uncertainty of 4 kcal mol -1 in the negative temperature coefficient region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Characterizing model uncertainties in simulated coast-to-offshore wind over the northeast U.S. using multi-platform measurements from the TCAP field campaign

Numerical weather prediction (NWP) models, such as the Weather Research and Forecasting (WRF) model, are widely used to provide estimates of the offshore wind energy resource owing to their large spatial coverage compared to available observations. Nevertheless, spatiotemporal distribution of model biases is highly dependent on factors including model configuration, location, and the interplay of multi-scale physical processes. Here, in this study, we focus on the characterization of model uncertainties in simulated coast-to-offshore winds over the northeast U.S., by varying sea surface temperature (SST) forcings, surface layer (SL) and planetary boundary layer (PBL) parameterizations, as well as identifying biases that may be directly passed from initial and boundary conditions. Multiple measurements, including aircraft data collected during the U.S. Department of Energy's Two-Column Aerosol Project (TCAP) experiment, are used to constrain the model results and facilitate quantitative comparisons. Our analysis indicates while SST forcing has notable impacts on simulated air temperature and moisture within PBL, the modeled winds are in general more sensitive to the choices of SL and PBL physics than to SST. The model’s forcing data not only controls the vertical dependence of wind speed errors, but also alters regional variability in wind speed’s spatial correlation. Bias comparisons between ERA5 reanalysis and ensemble simulations revealed significant similarity, particularly in wind speed biases during winter, underscoring their dependency on initial and boundary conditions. Coastal and offshore near-surface wind speed biases tend to exhibit much higher similarity in winter than in summer due to the presence of much stronger and more persistent synoptic wind conditions. This study highlights the importance of accurate atmospheric forcing and parameterization choices in improving wind forecasts and suggests the potential for extrapolating coastal wind biases to offshore locations, aiding wind energy forecasting and informing the Wind Forecast Improvement Project-3 (WFIP3).

17 WIND ENERGY↗
DOE OSTI2023

Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Data-driven upper bounds and event attribution for unprecedented heatwaves

The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot temperatures can become. Generalized Extreme Value theory provides a data-driven estimate of extreme thresholds; however, upper bounds may be exceeded by future events, which undermines attribution and planning for heatwave impacts. Here, we show how the occurrence and relative probability of observed yet unprecedented events that exceed a priori upper bound estimates, so-called “impossible” temperatures, has changed over time. We find that many unprecedented events are actually within data-driven upper bounds, but only when using modern spatial statistical methods. Furthermore, there are clear connections between anthropogenic forcing and the “impossibility” of the most extreme temperatures. Robust understanding of heatwave thresholds provides critical information about future record-breaking events and how their extremity relates to historical measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.

42 ENGINEERING↗
DOE OSTI2023

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

42 ENGINEERING↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗