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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 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 OSTI2022

Interpretable Uncertainty Quantification in AI for HEP

Estimating uncertainty is at the core of performing scientific measurements in HEP: a measurement is not useful without an estimate of its uncertainty. The goal of uncertainty quantification (UQ) is inextricably linked to the question, "how do we physically and statistically interpret these uncertainties?" The answer to this question depends not only on the computational task we aim to undertake, but also on the methods we use for that task. For artificial intelligence (AI) applications in HEP, there are several areas where interpretable methods for UQ are essential, including inference, simulation, and control/decision-making. There exist some methods for each of these areas, but they have not yet been demonstrated to be as trustworthy as more traditional approaches currently employed in physics (e.g., non-AI frequentist and Bayesian methods). Shedding light on the questions above requires additional understanding of the interplay of AI systems and uncertainty quantification. We briefly discuss the existing methods in each area and relate them to tasks across HEP. We then discuss recommendations for avenues to pursue to develop the necessary techniques for reliable widespread usage of AI with UQ over the next decade.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

CALPHAD Uncertainty Quantification and TDBX

CALPHAD uncertainty quantification (UQ) is the foundation of materials design with quantified confidence. We report a framework and software packages to enable CALPHAD UQ assessment and calculation using commercial CALPHAD software (Thermo-Calc). This Bayesian inference framework is coupled with a Markov chain Monte Carlo algorithm to establish uncertainty traces with a given thermodynamic database file (TDB) and corresponding experimental data points. This general framework is demonstrated with the Ni–Cr binary system. The algorithm is firstly validated on synthetic data with known ground truth. Then it is applied to real experimental data to generate posterior traces. We develop a file format named TDBX, which provides a single source of truth by combining the original TDB content and the traces for each assessed Gibbs energy parameter. CALPHAD UQ calculations are performed based on the TDBX file, from which uncertainties for phase boundaries, enthalpy curves, and solidification range are collected as examples of basic design parameters. This TDBX file with corresponding scripts are made open-source. Finally, the combination of CALPHAD UQ assessments and calculations connected by TDBX supports uncertainty-assisted modeling, enabling the integrated application of modern design with uncertainty methodologies to computational materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Deep neural network uncertainty quantification for LArTPC reconstruction

We evaluate uncertainty quantification (UQ) methods for deep learning applied to liquid argon time projection chamber (LArTPC) physics analysis tasks. As deep learning applications enter widespread usage among physics data analysis, neural networks with reliable estimates of prediction uncertainty and robust performance against overconfidence and out-of-distribution (OOD) samples are critical for their full deployment in analyzing experimental data. While numerous UQ methods have been tested on simple datasets, performance evaluations for more complex tasks and datasets are scarce. Here we assess the application of selected deep learning UQ methods on the task of particle classification using the PiLArNet monte carlo 3D LArTPC point cloud dataset. We observe that UQ methods not only allow for better rejection of prediction mistakes and OOD detection, but also generally achieve higher overall accuracy across different task settings. We assess the precision of uncertainty quantification using different evaluation metrics, such as distributional separation of prediction entropy across correctly and incorrectly identified samples, receiver operating characteristic curves (ROCs), and expected calibration error from observed empirical accuracy. We conclude that ensembling methods can obtain well calibrated classification probabilities and generally perform better than other existing methods in deep learning UQ literature.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Bi-fidelity variational auto-encoder for uncertainty quantification

Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the need for computational efficiency with the requirement for numerical accuracy. To address this trade-off, we propose a novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to estimate the uncertainty associated with a QoI from low-fidelity (LF) and high-fidelity (HF) samples of the QoI. Here, this model allows for the approximation of the statistics of the HF QoI by leveraging information derived from its LF counterpart. Specifically, we design a bi-fidelity auto-regressive model in the latent space which is integrated within the VAE’s probabilistic encoder–decoder structure. An effective algorithm is proposed to maximize the variational lower bound of the HF log-likelihood in the presence of limited HF data, resulting in the synthesis of HF realizations with a reduced computational cost. Additionally, we introduce the concept of the bi-fidelity information bottleneck (BF-IB) to provide an information-theoretic interpretation of the proposed BF-VAE model. Our numerical results demonstrate that the BF-VAE leads to considerably improved accuracy, as compared to a VAE trained using only HF data, when limited HF data is available.

42 ENGINEERING↗
DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗
DOE OSTI2025

Uncertainty Quantification for Neutron Shield Using Convolutional Neural Networks

Uncertainty quantification from radiation transport calculations was conducted using a Bayesian inference approach. A surrogate model, using a convolutional neural network, was employed to emulate the neutron fluence, which was simulated with a Monte Carlo radiation transport model. This allowed for a computationally cheap approach to evaluate input parameters and to sample their corresponding posterior probability distributions. Experimental data from the literature were employed to perform uncertainty quantification studies for concrete shields. As a result, the method is a nonintrusive approach that enables studies with multiple input parameters and can be applied to any radiation transport model.

Bayesian inference↗
DOE OSTI2025

The Fluid Dynamics Uncertainty Quantification Challenge Problem: XFOIL vs. MFOIL

Uncertainty quantification (UQ) has become more critical in aerospace engineering due to the growing dependence on computational tools for design optimization and performance analyses of aerospace vehicles. Even though the significance of UQ in assessing the credibility of computational analyses is well recognized, its costs and complexity impede its integration into standard practices, particularly in computational fluid dynamics (CFD) and other fluid analyses. This paper presents a UQ study for low-fidelity computational aerodynamics analyses with XFOIL and mfoil (i.e., the MATLAB version of XFOIL with several implementation modifications); these tools are utilized widely in both research and education. The main contributions of this paper are as follows: 1) improved precision in quantifying the uncertainty of the baseline Monte Carlo results used to benchmark surrogate modeling techniques for UQ, 2) quantification of the effect of the implementation differences between XFOIL and mfoil on solution quantities of interest (QoIs), such as lift and pitching moment coefficients, and 3) development of an open-source UQ library for use with XFOIL and mfoil, which has educational values and helps promote UQ for fluid analyses with aerospace applications. Results and discussions revolve around cases 1-4 of the challenge problem posed by the AIAA Fluid Dynamics Technical Committee’s Uncertainty Quantification Discussion Group (UQDG). In case 3, this work employs CFDverify, an open-source solution verification software, to quantify the discretization error and evaluate the extrapolated QoIs based on the grid convergence index (GCI). This UQ study differentiates itself from previous studies in the rigor of handling baseline Monte Carlo uncertainty and in including mfoil, which is a more accessible alternative to XFOIL. Finally, despite the growing computing power, low-fidelity computational tools remain valuable, such as for aerodynamic shape optimization at Mach numbers below 0.65 and low-to-mid Reynolds numbers.

Lay, Aidan S [University of Tennessee, Knoxville (↗
DOE OSTI2023

Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling

Abstract. Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estimation. While simple to implement, MC estimation fails to provide reliable information about statistical quantities (such as the expected value of the output of interest) in application settings such as climate modeling, for which obtaining a single realization of the output of interest is a costly endeavor. Specifically, the dilemma encountered is that many samples of the output of interest have to be collected in order to obtain an MC estimator that has sufficient accuracy – so many, in fact, that the available computational budget is not large enough to effect the number of samples needed. To circumvent this dilemma, we consider using multifidelity Monte Carlo (MFMC) estimation which leverages the use of less costly and less accurate surrogate models (such as coarser grids, reduced-order models, simplified physics, and/or interpolants) to achieve, for the same computational budget, higher accuracy compared to that obtained by an MC estimator – or, looking at it another way, an MFMC estimator obtains the same accuracy as the MC estimator at lower computational cost. The key to the efficacy of MFMC estimation is the fact that most of the required computational budget is loaded onto the less costly surrogate models so that very few samples are taken of the more expensive model of interest. We first provide a more detailed discussion about the need to consider an alternative to MC estimation for uncertainty quantification. Subsequently, we present a review, in an abstract setting, of the MFMC approach along with its application to three climate-related benchmark problems as a proof-of-concept exercise.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Economic Parameter Uncertainty Quantification Demonstration

HERON has recently added uncertainty quantification capabilities for economic parameters. Users may now associate a distribution with certain cash flow parameters to simulate uncertainty in cost or other economic inputs. For example, a user may want to capture the uncertainty of capital expenditures of an advanced nuclear power plant because public data is hard to find or is not available yet. This new addition allows users to account for that uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

On the Need to Align Intent and Implementation in Uncertainty Quantification for Machine Learning

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and estimation across disciplines, and (b) the varying technical requirements for establishing trustworthy uncertainties in diverse problem contexts. In this position paper, we aim to clarify the depth of these challenges by identifying these inconsistencies and articulating how different contexts impose distinct epistemic demands. We examine the current landscape of estimation targets (e.g., prediction, inference, simulation-based inference), uncertainty constructs (e.g., frequentist, Bayesian, fiducial), and the approaches used to map between them. Drawing on the literature, we highlight and explain examples of problematic mappings. To help address these issues, we advocate for standards that promote alignment between the \textit{intent} and \textit{implementation} of uncertainty quantification (UQ) approaches. We discuss several axes of trustworthiness that are necessary (if not sufficient) for reliable UQ in ML models, and show how these axes can inform the design and evaluation of uncertainty-aware ML systems. Our practical recommendations focus on scientific ML, offering illustrative cases and use scenarios, particularly in the context of simulation-based inference (SBI).

Trivedi, Shubhendu [MIT] (ORCID:0000000312374301)↗
DOE OSTI2025

Dataset for "Machine Learning Ensembles Can Enhance Hydrologic Predictions and Uncertainty Quantification" Willard et al. (2025).

This data release provides all data and code used in the paper " "Machine Learning Ensembles Can Enhance Hydrologic Predictions and Uncertainty Quantifications" Willard et al. (2025)" to model stream temperature, evaluate, and assess results. The associated manuscript explores the effect of different ensemble construction techniques across different common machine learning (ML) architectures for predictions in unmonitored basins. Modeling was done using long short-term memory (LSTM), gated recurrent unit (GRU), temporal convolution network (TCN), and extreme gradient boosting (XGBoost) models, and stream site coverage spans 1362 locations across the conterminous United States. The ensemble construction techniques investigated include ensemble by random weight initialization, differing hyperparameters, different random subsets of training data, different subselections of input features, different architectures, and Monte Carlo Dropout. The data is organized into these items items:Code repository and data for the paper " "Machine Learning Ensembles Can Enhance Hydrologic Predictions and Uncertainty Quantifications" Willard et al. (2025).Code: stream_temp_ml_regionalization.zip contains the code repositoryData to run the code:- data_dir.zip -- contains all files that should be moved to the "DATA_DIR" variable defined in the "set_env_vars.sh" script in the code repository- metadata_dir.zip -- contains all files that should be moved to the "METADATA_DIR" variable defined in the "set_env_vars.sh" script in the code repositoryData produced by the code and used in the paper:- outputs_dir.zip - contains model output and results (outputs_dir/results), model weights (outputs_dir/models), and all other outputs used for the paper including feature importances.To cite this code, please use the following BibTeX or MLA entries:bibtex:@misc{willard2025streamensembles,author = {Jared Willard and Charuleka Varadharajan},title = {Dataset for "Machine Learning Ensembles Can Enhance Hydrologic Predictions and Uncertainty Quantification"},year = {2024},doi = {10.15485/2527393},publisher = {ESS-DIVE Repository},url = {https://data.ess-dive.lbl.gov/datasets/doi:10.15485/2527393}}MLA: Willard, Jared, et al. Dataset for "Machine Learning Ensembles Can Enhance Hydrologic Predictions and Uncertainty Quantification". 2025. ESS-DIVE Repository, doi:10.15485/2448016.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Radiation image reconstruction and uncertainty quantification using a Gaussian process prior

We propose a complete framework for Bayesian image reconstruction and uncertainty quantification based on a Gaussian process prior (GPP) to overcome limitations of maximum likelihood expectation maximization (ML-EM) image reconstruction algorithm. The prior distribution is constructed with a zero-mean Gaussian process (GP) with a choice of a covariance function, and a link function is used to map the Gaussian process to an image. Unlike many other maximum a posteriori approaches, our method offers highly interpretable hyperparamters that are selected automatically with the empirical Bayes method. Furthermore, the GP covariance function can be modified to incorporate a priori structural priors, enabling multi-modality imaging or contextual data fusion. Lastly, we illustrate that our approach lends itself to Bayesian uncertainty quantification techniques, such as the preconditioned Crank–Nicolson method and the Laplace approximation. The proposed framework is general and can be employed in most radiation image reconstruction problems, and we demonstrate it with simulated free-moving single detector radiation source imaging scenarios. We compare the reconstruction results from GPP and ML-EM, and show that the proposed method can significantly improve the image quality over ML-EM, all the while providing greater understanding of the source distribution via the uncertainty quantification capability. Furthermore, significant improvement of the image quality by incorporating a structural prior is illustrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps and constitutive models simultaneously is currently lacking. Further, this paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

MULTI-FIDELITY MODELING AND UNCERTAINTY QUANTIFICATION OF INVERTER BASED RESOURCES IN INTEGRATED T&D SYSTEMS

Uncertainty quantification plays a pivotal role in improving the accuracy and reliability of inverter operation within modern power systems that are increasingly dominated by inverter-based resources (IBRs). IBRs, especially those operating under grid forming (GFM) control, rely heavily on a complex set of control parameters and system measurements to maintain voltage, frequency, and power balance. Traditional deterministic modeling approaches often fail to capture these parameter deviations, potentially resulting in suboptimal control actions, reduced system stability, or even instability under high penetration of IBRs. In this paper, we demonstrate the application of model calibration and uncertainty quantification (UQ) principles to an integrated transmission and distribution (T&D) model involving a GFM converter and provide a framework for prioritizing control improvements, guiding robust design, and informing adaptive strategies that can accommodate real-time variability in system conditions. The proposed approach could be valuable in enhancing the robustness of current and future power systems under increased IBR penetrations.

24 POWER TRANSMISSION AND DISTRIBUTION↗