SEARCH · Engineering Papers

Results for “UQ”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Evaluating probabilistic deep learning methods for uncertainty quantification of temperature downscaling

Deep learning (DL) has emerged as a promising tool for downscaling coarse-resolution climate data to high-resolution outputs, enabling improved regional climate predictions. A critical aspect of DL-based downscaling is the incorporation of uncertainty quantification (UQ), which enhances the interpretability and reliability of predictions—key factors for climate risk assessment and decision-making. This study develops a DL model to downscale 2 m temperature across the contiguous United States using reanalysis datasets. We systematically evaluate three epistemic UQ methods—deep ensembles (DEns), Monte Carlo dropout (MCD), and Flipout—based on their probabilistic accuracy, downscaling performance, sensitivity to geographical features, and computational efficiency. Results indicate that MCD generally outperforms Flipout and DEns in terms of calibration and downscaling accuracy. However, DEns demonstrate lower calibration errors in coastal regions, indicating its higher confidence within these areas. Flipout, in contrast, is more sensitive to elevation gradients and exhibits higher calibration errors in mountainous regions. Hence, the choice of UQ method for this task depends on the specific requirements of the application. For applications that prioritize overall calibration, downscaling accuracy, and computational efficiency, MCD is a strong candidate. These findings highlight the importance of selecting UQ methods based on application-specific requirements, such as geographical context and computational constraints. By addressing the trade-offs between UQ methods, this study provides actionable insights for improving the reliability, scalability, and utility of DL-based downscaling in climate science.

Environmental sciences↗

DOE OSTI2025

Evaluating Probabilistic Deep Learning Methods for Uncertainty Quantification of Precipitation Bias Correction

Climate models often exhibit biases in their precipitation predictions, particularly underestimating high-intensity events and overestimating low precipitation. Deep learning approaches offer promising solutions, but their epistemic uncertainty associated with a deep learning–based bias correction method has not previously been quantified for reliable downstream climate impact studies. While methods for capturing the epistemic uncertainty in deep learning frameworks exist, there is currently no consensus on the best method. In this work, we compare three uncertainty quantification (UQ) methods—Deep Ensembles (DEns), Monte Carlo Dropout (MCD), and Flipout—by assessing the reliability of their uncertainty estimates using standard measures such as sharpness and calibration. These UQ methods are applied to an existing deep learning precipitation bias correction model known as UFNet: a coupled U-Net and fully connected neural network. The methods utilized to assess the models’ uncertainties are 1) calibration, which ensures that the expected probabilities of the model align with reality and 2) sharpness, which is a measure of the precision of the model’s probabilistic predictions. Of the three UQ methods evaluated, the DEns and MCD methods demonstrated the best-calibrated performance (expected calibration error of 0.36 and 0.35, respectively), compared to Flipout (0.58). In contrast, Flipout had the sharpest predictions and the highest metric performance in bias correcting precipitation—especially for higher-order moments such as kurtosis with a spatial correlation of 72% compared to 32% and 55% spatial correlation for DEns and MCD, respectively. Of the three UQ methods, MCD was found to be the most suitable method for UQ purposes based on its calibration, sharpness, and computational requirements.

Bayesian methods↗

NASA NTRS2019

Uncertainty Quantification for JPL Retrievals

We define the notions of verification, validation, and uncertainty quantification (VVUQ), and place them in the context of retrievals of Earth science data. Uncertainty quantification (UQ) is the process of characterizing the uncertainty of a measurement system relative to the true, physical quantity it measures. UQ is needed when measurements are used for scientific inference, assimilated into models with other data, and used for decision-making and risk analysis. Many measurements come with measures of standard error and bias, but these uncertainty measures are often inaccurate, due to the operational need to assume crisp values for parameters which are in fact uncertain, as well as the failure of technical assumptions needed by operational error-estimation approaches. UQ provides a way to study which assumptions fail to hold, and a tool to improve the measurement. We describe a particular, broadly-applicable UQ setup that has been successful for JPL retrievals including OCO-2, and provide recommendations for furthering the UQ state of the practice at JPL.

Turmon, Michael↗

NASA NTRSDate not supplied

Integration of Uncertainty Quantification in a Model-Based Systems Analysis and Engineering Framework

This paper presents a technical approach to improve the confidence in the systems analysis process by integrating Uncertainty Quantification (UQ) techniques within a Model-Based Systems Analysis and Engineering (MBSA&E) framework. The MBSA&E architecture uses system models and multidisciplinary analytical solutions as central artifacts for system design and analysis. The integration of UQ enables engineers to assess and mitigate uncertainties associated with a system model, design parameters, and constraint inputs, leading to more complete design studies and further informed decision-making processes. The proposed approach leverages the strengths of MBSA&E and extends it with a UQ methodology to quantify uncertainties in the input parameters and to trace the uncertainties as they propagate throughout the system model. To demonstrate the effectiveness of an integrated MBSA&E-UQ approach, a case study involving a simplified analysis of a Transonic Truss-Braced Wing (TTBW) concept vehicle is performed. This integration enables a more comprehensive evaluation of system performance and behavior under uncertainty and a more robust approach for system design and analysis. Lastly, the paper addresses the challenges and considerations associated with integrating UQ into an MBSA&E framework.

systems analysis↗

NASA NTRSDate not supplied

Integration of Uncertainty Quantification in a Model-Based Systems Analysis and Engineering Framework

systems analysis↗

DOE OSTI2025

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials

Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Towards a Robust Adaptive Digital Twin for Fusion Applications

The development of a digital twin system for fusion applications is essential for enhancing the prediction, analysis, and optimization of complex plasma processes. Machine learning (ML), particularly deep learning has demonstrated strong capabilities in modeling such highly nonlinear and intricate systems. However, two critical challenges limit the deployment of deep learning-based digital twins: Uncertainty Quantification (UQ) and data drift. UQ is vital for ensuring trustworthy predictions, especially in decision-support scenarios. Additionally, data-driven models are often sensitive to changes in the underlying data distribution, such as shot-to-shot variations in fusion experiments, which can lead to performance degradation over time. To address these challenges, we are developing an uncertainty-aware, adaptive digital twin framework. Our approach incorporates deep learning models enhanced with Gaussian Process approximations for predictive uncertainty estimation, coupled with an online learning mechanism that enables continuous model adaptation to new experimental data. This adaptive capability allows the data driven models to respond effectively to evolving plasma behaviors and equipment conditions. Specifically, to mitigate the effects of shot-to-shot drift, our system updates itself incrementally as new data becomes available, improving both robustness and fidelity. Our vision is to evolve this data driven model into a self-sustaining digital twin system that leverages UQ based feedback to continuously refine itself and potentially support real-time decision making. This presentation will cover a brief background on uncertainty quantification for ML, our ongoing effort on development of UQ capabilities for ML, our data science pipeline from data collection to model development and analysis and online learning framework for modeling coil deflection at DIII-D. I will also briefly touch upon opportunities and challenges in development of digital twin framework.

Sammuli, Brian [General Atomics]↗

DOE OSTI2024

DeepUQ: Assessing the Aleatoric Uncertainties from two Deep Learning Methods

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret exactly. We systematically compare aleatoric uncertainty measured by two UQ techniques, Deep Ensembles (DE) and Deep Evidential Regression (DER). Our method focuses on both zero-dimensional (0D) and two-dimensional (2D) data, to explore how the UQ methods function for different data dimensionalities. We investigate uncertainty injected on the input and output variables and include a method to propagate uncertainty in the case of input uncertainty so that we can compare the predicted aleatoric uncertainty to the known values. We experiment with three levels of noise. The aleatoric uncertainty predicted across all models and experiments scales with the injected noise level. However, the predicted uncertainty is miscalibrated to $\rm{std}(\sigma_{\rm al})$ with the true uncertainty for half of the DE experiments and almost all of the DER experiments. The predicted uncertainty is the least accurate for both UQ methods for the 2D input uncertainty experiment and the high-noise level. While these results do not apply to more complex data, they highlight that further research on post-facto calibration for these methods would be beneficial, particularly for high-noise and high-dimensional settings.

Nevin, Rebecca↗

DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Bayesian discovery of optimal reduced order models from mechanistic and experimental data: A case study of Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles rely on a silicon carbide (SiC) layer as the primary structural material and barrier to metallic fission products (FPs) release. Accurate prediction of palladium (Pd) transport and penetration is therefore critical for qualifying TRISO fuels for advanced reactors. The empirical correlation for Pd penetration in BISON is derived from historical particle-fuel data, but cannot explain the large scatter in the experimental data that arises from varying experimental conditions. To aid fuel qualification, we previously developed a mechanistic reduced order model (ROM) using BISON that resolves these dependencies. Here, in this work we build on that mechanistic ROM and perform validation and quantify its uncertainty using Bayesian uncertainty quantification (UQ). calibration against a suite of in-pile and out-of-pile experiments spanning particle compositions, geometries, and operating conditions, and we benchmark it against the empirical correlation. Bayesian UQ identifies influential parameters, calibrates them to data, and yields predictive intervals. Results show that while the empirical correlation can be tuned to fit a single experiment type, it transfers poorly; the mechanistic ROM sustains accuracy with credible uncertainty across disparate conditions. This demonstrates a practical path—via Bayesian UQ applied to mechanistic ROMs—to leverage single-effect experiments for inferring in-reactor behavior and supporting TRISO fuel qualification.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

An uncertainty visualization framework for large-scale cardiovascular flow simulations: A case study on aortic stenosis

We present a generalizable uncertainty quantification (UQ) and visualization framework for lattice Boltzmann method simulations of high Reynolds number vascular flows, demonstrated on a patient-specific stenosed aorta. The framework combines EasyVVUQ for parameter sampling with large-eddy simulation turbulence modeling in HemeLB, and executes ensembles on the Frontier exascale supercomputer. Spatially resolved metrics, including entropy and isosurface-crossing probability, are used to map uncertainty in pressure and wall shear stress fields directly onto vascular geometries. Two sources of model variability are examined: inlet peak velocity and the Smagorinsky constant. Inlet velocity variation produces high uncertainty downstream of the stenosis where turbulence develops, while upstream regions remain stable. Smagorinsky constant variation has little effect on the large-scale pressure field but increases WSS uncertainty in localized high-shear regions. In both cases, the stenotic throat manifests low entropy, indicative of robust identification of elevated WSS. By linking quantitative UQ measures to three-dimensional anatomy, the framework improves interpretability over conventional 1D UQ plots and supports clinically relevant decision-making, with broad applicability to vascular flow problems requiring both accuracy and spatial insight.

Hemodynamics↗

DOE OSTI2024

Uncertainty quantification for molecular property predictions with graph neural architecture search

Graph Neural Networks (GNNs) have emerged as a prominent class of data-driven methods for molecular property prediction. However, a key limitation of typical GNN models is their inability to quantify uncertainties in the predictions. This capability is crucial for ensuring the trustworthy use and deployment of models in downstream tasks. To that end, we introduce AutoGNNUQ, an automated uncertainty quantification (UQ) approach for molecular property prediction. AutoGNNUQ leverages architecture search to generate an ensemble of high-performing GNNs, enabling the estimation of predictive uncertainties. Our approach employs variance decomposition to separate data (aleatoric) and model (epistemic) uncertainties, providing valuable insights for reducing them. In our computational experiments, we demonstrate that AutoGNNUQ outperforms existing UQ methods in terms of both prediction accuracy and UQ performance on multiple benchmark datasets, and generalizes well to out-of-distribution datasets. Additionally, we utilize t-SNE visualization to explore correlations between molecular features and uncertainty, offering insight for dataset improvement. AutoGNNUQ has broad applicability in domains such as drug discovery and materials science, where accurate uncertainty quantification is crucial for decision-making.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Uncertainty-Aware and Explainable Human Error Detection in the Operation of Nuclear Power Plants

The timely and accurate identification of incidents, such as human factor error, is important to restore nuclear power plants (NPPs) to a stable state. However, the identification of abnormal operating conditions is difficult because of the existence of multiple scenarios. In addition, to implement mitigation actions rapidly after an incident occurs, operators must accurately identify an incident by monitoring the trends of many variables. The mental burden posed by this can increase human error and cause failure in identifying incidents. Failure to identify incidents directly results in erroneous mitigation measures, which are detrimental to NPPs. In this study, we leverage uncertainty-aware models to identify such errors and thereby increase the chances of mitigating them. We use the data collected from a physical test bed. The goal is to identify both certain and accurate models. For this, the two main aspects of focus in this study are explainable artificial intelligence (XAI) and uncertainty quantification (UQ). While XAI elucidates the decision pathway, UQ evaluates decision reliability. Their integration paints a comprehensive picture, signifying that understanding decisions and their confidence should be interlinked. Thus, in this study we leverage UQ measures (e.g. entropy and mutual information) along with Shapley additive explanations to gain insights into the features contributing to both accuracy and uncertainty in error identification. Furthermore, our results show that uncertainty-aware models combined with XAI tools can explain the artificial intelligence–prescribed decisions, with the potential of better explaining errors for the operators.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov–Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage.} Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to significantly improve the reliability and applicability of KANs in scientific machine learning.

• Artificial intelligence (AI) / machine learning ↗

DOE OSTI2024

Uncertainty Quantification and Sensitivity Analysis of Low-Dimensional Manifold via Co-Kurtosis PCA in Combustion Modeling

For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗