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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 OSTI2023

Benchmarking FFTF LOFWOS Test# 13 using SAM code: Baseline model development and uncertainty quantification

The development and deployment of advanced reactors, such as the sodium-cooled fast reactor (SFR), relies on sophisticated modeling tools to ensure the safety of the design under various transients. The predictive capability of these advanced modeling tools requires validation to garner trust in supporting the licensing of the advanced reactors. For this reason, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13.In this study, we present and discuss the benchmarking efforts of the modern system code SAM on the FFTF LOFWOS Test #13. Further, the SAM baseline model was developed according to the benchmark specification, which included a detailed core model with reactivity feedback. Generally, good agreement was observed between the baseline results and benchmark measurements; however, discrepancies persisted, particularly in predicted fuel assembly coolant outlet temperatures. Utilizing the baseline model, uncertainty quantification (UQ) and sensitivity analysis (SA) were conducted with the assistance of various statistical learning and machine learning methods, including kernel density estimation, Gaussian processes, and Sobol indices. Following the baseline model prediction and UQ and SA results, we discuss the reasons for the simulation discrepancies and propose further improvements to the model. This benchmarking effort adheres to the best-estimate plus uncertainty approach and can serve as a valuable example for supporting risk-informed licensing of advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Predicting critical heat flux with uncertainty quantification and domain generalization using conditional variational autoencoders and deep neural networks

Deep generative models (DGMs) can generate synthetic data samples that closely resemble the original dataset, addressing data scarcity. In this work, we developed a conditional variational autoencoder (CVAE) to augment critical heat flux (CHF) data used for the 2006 Groeneveld lookup table. To compare with traditional methods, a fine-tuned deep neural network (DNN) regression model was evaluated on the same dataset. Both models achieved small mean absolute relative errors, with the CVAE showing more favorable results. Uncertainty quantification (UQ) was performed using repeated CVAE sampling and DNN ensembling. The DNN ensemble improved performance over the baseline, while the CVAE maintained consistent results with less variability and higher confidence. Both models achieved small errors inside and outside the training domain, with slightly larger errors outside. Altogether, the CVAE performed better than the DNN in predicting CHF and exhibited better uncertainty behavior.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Physics-based hybrid machine learning for critical heat flux prediction with uncertainty quantification

Critical heat flux (CHF) is a key quantity in nuclear system modeling due to its impact on heat transfer, safety margins, and reactor performance. This study develops and validates an uncertainty-aware hybrid modeling approach that combines machine learning with physics-based models to predict CHF in cases of dryout. The Biasi and Bowring empirical correlations were paired with three ML uncertainty quantification (UQ) techniques: deep neural network (DNN) ensembles, Bayesian neural networks (BNNs), and deep Gaussian processes (DGPs). A pure ML model without a base model was evaluated for comparison. Model performance was assessed under plentiful (7,350 points) and limited (9 points) training data scenarios using parity, uncertainty distributions, and calibration curves. Results show that the Biasi hybrid DNN ensemble achieved the best overall performance, with a mean absolute relative error of 1.846%, and well-calibrated uncertainty estimates. The BNN-based hybrids showed slightly higher error (2.14%) but superior uncertainty calibration. DGP models underperformed, with over 6% error and poor uncertainty calibration. All hybrid models outperformed pure machine learning configurations, demonstrating resistance against data scarcity. These findings indicate that hybrid modeling significantly improves predictive accuracy, interpretability, and resilience to data scarcity. The integration of uncertainty awareness provides actionable confidence in CHF predictions, which is vital for safety-critical decisions in nuclear applications. This hybrid approach offers a viable pathway for deploying ML models in reactor analysis tools while preserving domain knowledge and physical consistency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Thermodynamic modeling of the Nb-Ni system with uncertainty quantification using PyCalphad and ESPEI

Here, the Nb–Ni system is remodeled with uncertainty quantification (UQ) using software tools of PyCalphad and ESPEI (the Extensible, Self-optimizing Phase Equilibria Infrastructure) with the presently implemented capability of modeling site fraction based on Wyckoff positions. The five- and three-sublattice models are used to model the topologically close pack (TCP) μ-Nb 7 Ni 6 and δ-NbNi 3 phases according to their Wyckoff positions. The inputs for CALPHAD-based thermodynamic modeling include the thermochemical data as a function of temperature predicted by first-principles and phonon calculations based on density functional theory (DFT), ab initio molecular dynamics (AIMD) simulations, together with phase equilibrium and site fraction data in the literature. In addition to phase diagram and thermodynamic properties, the CALPHAD-based predictions of site fractions of Nb in μ-Nb 7 Ni 6 agree well with experimental data. Furthermore, the UQ estimation using the Markov Chain Monte Carlo (MCMC) method as implemented in ESPEI is applied to study the uncertainty of site fraction in μ-Nb 7 Ni 6 and enthalpy of mixing (ΔH mix ) in liquid.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Bottom-up and Top-Down Uncertainty Quantification for Measurements

Several recent papers address improved uncertainty quantification (UQ) for measurements used in nuclear safeguards. This paper reviews progress and presents new results for bottom-up (first principles) and top-down (empirical) UQ for safeguards, where the main quantitative measure of uncertainty is the total measurement error standard deviation (SD), which includes both random and systematic error components. The five main UQ topics addressed here include: (1) impact of making data-driven choices in SD estimation; (2) use of approximate Bayesian computation (ABC) for both bottom-up and top-down UQ; (3) computational calibration; (4) revisions to the guide to the expression of uncertainty in measurement (GUM), and (5) critique of a recently-suggested “Unified Theory of Measurement Errors and Uncertainties.”

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2020

GMRES with embedded ensemble propagation for the efficient solution of parametric linear systems in uncertainty quantification of computational models

In a previous work, embedded ensemble propagation was proposed to improve the efficiency of sampling-based uncertainty quantification methods of computational models on emerging computational architectures. It consists of simultaneously evaluating the model for a subset of samples together, instead of evaluating them individually. A first approach introduced to solve parametric linear systems with ensemble propagation is ensemble reduction. In Krylov methods for example, this reduction consists in coupling the samples together using an inner product that sums the sample contributions. Ensemble reduction has the advantages of being able to use optimized implementations of BLAS functions and having a stopping criterion which involves only one scalar. However, the reduction potentially decreases the rate of convergence due to the gathering of the spectra of the samples. In this paper, we investigate a second approach: ensemble propagation without ensemble reduction in the case of GMRES. This second approach solves each sample simultaneously but independently to improve the convergence compared to ensemble reduction. This raises two new issues which are solved in this paper: the fact that optimized implementations of BLAS functions cannot be used anymore and that ensemble divergence, whereby individual samples within an ensemble must follow different code execution paths, can occur. We tackle those issues by implementing a high-performing ensemble GEMV and by using masks. The proposed ensemble GEMV leads to a similar cost per GMRES iteration for both approaches, i.e. with and without reduction. For illustration, we study the performances of the new linear solver in the context of a mesh tying problem. Furthermore, this example demonstrates improved ensemble propagation speed-up without reduction.

BLAS↗
DOE OSTI2023

Multifidelity uncertainty quantification with models based on dissimilar parameters

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parameterization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method (Tipireddy and Ghanem, 2014). The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. Here we present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity (HF) data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parameterization.

42 ENGINEERING↗
DOE OSTI2020

Stochastic nonlinear analysis of unidirectional fiber composites using image-based microstructural uncertainty quantification

Here, we present a data-driven nonlinear uncertainty quantification and propagation framework to study the microstructure-induced stochastic performance of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The proposed approach integrates (1) microscopic image characterization, (2) stochastic microstructure reconstruction, and (3) efficient multiscale finite element simulations enabled by self-consistent clustering (SCA) analysis. To model the complex microstructural variability, the proposed UQ methods take the non-Gaussian uncertainty sources into account through a distribution-free sampling approach leveraging nonparametric and asymptotic statistical tools. A hierarchical conditional sampling strategy enables the simultaneous sampling of multiple sources of uncertainties. Our approach provides insights into the impact of microstructural variabilities, which are shown to have an increasing impact on the nonlinear responses of UD CFRP parts under progressive compression loading and ultimately on the failure rate over time. We discover that before CFRP parts start to fail, a characteristic time period emerges with distinctive uncertainty distributions specific to the microstructure variability and the probability of failure. Identifying the failure time period is crucial to the reliability prediction, which is an essential component of CFRP design.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

PyApprox: A software package for sensitivity analysis, Bayesian inference, optimal experimental design, and multi-fidelity uncertainty quantification and surrogate modeling

PyApprox is a Python-based one-stop-shop for probabilistic analysis of numerical models such as those used in the earth, environmental and engineering sciences. Easy to use and extendable tools are provided for constructing surrogates, sensitivity analysis, Bayesian inference, experimental design, and forward uncertainty quantification. The algorithms implemented represent a wide range of methods for model analysis developed over the past two decades, including recent advances in multi-fidelity approaches that use multiple model discretizations and/or simplified physics to significantly reduce the computational cost of various types of analyses. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of new or existing algorithms for a wide range of model analyses. Here, this paper introduces PyApprox and its various features, and presents results demonstrating the utility of PyApprox on a benchmark problem modeling the advection of a tracer in groundwater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Explainable machine learning model for multi-step forecasting of reservoir inflow with uncertainty quantification

We propose an explainable machine learning (ML) model with uncertainty quantification (UQ) to improve multi-step reservoir inflow forecasting. Traditional ML methods have challenges in forecasting inflows multiple days ahead, and lack explainability and UQ. To address these limitations, we introduce an encoder–decoder long short-term memory (ED-LSTM) network for multi-step forecasting, employ the SHapley Additive exPlanation (SHAP) technique for understanding the influence of hydrometeorological factors on inflow prediction, and develop a novel UQ method for prediction trustworthiness. We apply these methods to forecast 7-day inflow in snow-dominant and rain-driven reservoirs. The results demonstrate the effectiveness of the ED-LSTM model, with high forecasting accuracy for short lead times. Our UQ method provides reliable uncertainty estimates, covering 90% of data with a 90% confidence level. The SHAP analysis reveals the importance of historical inflow and precipitation as influential factors. These findings and methods may support reservoir operators in optimizing water resources management decisions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Uncertainty quantification of the convolutional neural networks on permeability estimation from micro-CT scanned sandstone and carbonate rock images

Rock permeability is one of the most crucial properties affecting subsurface fluid flow behaviors. To accurately and robustly estimate the permeability, Digital Rock Physics, including micro-CT scanning technology and direct flow simulations on scanned images, has prevailed in recent years. Besides, machine learning techniques such as convolutional neural networks (CNNs) have been widely adopted and achieved success in permeability estimations directly from rock images. However, existing ML methods used for permeability estimation from rock images lack uncertainty quantification that causes unreliable predictions and overconfident estimations on out-of-distribution (OOD) samples. Here, in this work, we propose a PI3NN-CNN framework to address this problem. PI3NN-CNN consists of a CNN model for absolute permeability estimation and a PI3NN method to quantify the estimation uncertainty. It is able to quantify the uncertainty for in-distribution (InD) data with a desired confidence level, and identify OOD samples to avoid overconfident predictions. We demonstrate the method using micro-CT scanned images from two sandstone and two carbonate rocks. We found that PI3NN-CNN generates accurate predictions for InD samples, while producing high-quality prediction uncertainties regardless of the prediction accuracy. Meanwhile, PI3NN-CNN identifies OOD samples using its special network initialization scheme. The unique feature of PI3NN-CNN makes it applicable to more complex real-world image-based data for robust learning and predictions without overconfident estimations when the ground-truth information is unavailable.

58 GEOSCIENCES↗
DOE OSTI2020

On the quantification and efficient propagation of imprecise probabilities with copula dependence

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. Here, a hierarchical Bayesian multimodel approach is proposed to quantify uncertainty in dependence model-form and model parameters that result from small data sets. This approach begins by identifying, through Bayesian multimodel inference, a set of candidate marginal models and their corresponding model probabilities, and then estimating the uncertainty in the copula-based dependence structure, which is conditional on the marginals and their parameters. The overall uncertainties integrating marginals and copulas are probabilistically represented by an ensemble of multivariate candidate densities. A novel importance sampling reweighting approach is proposed to efficiently propagate the overall uncertainties through a computational model. Through an example studying the influence of constituent properties on the out-of-plane properties of transversely isotropic E-glass fiber composites, we show that the composite property with copula-based dependence model converges to the true estimate as data set size increases, while an independence or arbitrary Gaussian correlation assumption leads to a biased estimate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2023

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗