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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 OSTI2025

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗
NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗
DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Resilience-based Recovery Scheduling of Transportation Network in Mixed Traffic Environment: A Deep-Ensemble-Assisted Active Learning Approach

Devising effective post-hazard recovery strategies is critical in enhancing the resilience of transportation networks (TNs). However, existing work does not consider the multiclass users’ travel behavior in network functionality quantification and the metaheuristic solution procedures often suffer from extensive computational burden due to the exploration need in large solution space and the expensive functionality quantification. Here, this study develops a bilevel decision-making framework for the resilience-based recovery scheduling of the TN in a mixed traffic environment with connected and autonomous vehicles (CAVs) and human-driven vehicles (HDVs). The lower level quantifies the TN's functionality over time considering different travel behavior of CAV and HDV users arisen from their different levels of information perception. The upper level presents a novel deep-ensemble-assisted active learning approach to balance optimization performance and computational cost. This framework can help decision makers better quantify the TN's functionality to support effective recovery scheduling of TN with different mixed traffic scenarios ranging from HDV-only to future CAV-dominant traffic. The optimization approach bears the potential to be extended to solving general large-scale network recovery scheduling problems effectively and efficiently. The proposed methodology is demonstrated using a real-world traffic network in Southern California under earthquake considering deterministic and stochastic repair durations.

42 ENGINEERING↗
DOE OSTI2022

Paw-Net: Stacking ensemble deep learning for segmenting scanning electron microscopy images of fine-grained shale samples

Segmentation of scanning electron microscopy (SEM) images is critical yet time-consuming for geological analyses, as it needs to differentiate the boundaries for different mineral objects to facilitate subsequent analyses, such as porosity calculation. Recently, various machine learning methods, especially convolutional neural networks (CNNs), have been explored to segment SEM images of fine-grained shale samples. However, we found that general CNNs do not yield optimal performance due to insufficient training data and imbalanced objects in SEM images. This work has revised the U-Net architecture, a popular approach for biomedical image analyses, by incorporating a loss function that addresses the imbalance issue. Furthermore, we used the ensemble learning method to train multiple models and combined the results to improve the overall performance of segmentation. We prepared 2162 sub-images from raw SEM images in our experiments and divided them into training, validation, and testing datasets. The overall results show that our method improves the average Intersection over Union (IOU) of mineral objects from 0.49 to 0.58, compared to the original U-Net model. Our method can clearly distinguish each object from others with boundaries, even in highly imbalanced images. Training our models takes less than three minutes using a single GPU, while manual labeling can take up to three hours for each image. Furthermore, the method helps geoscientists gain insights quickly and effectively by building neural network models from a small dataset of SEM images.

58 GEOSCIENCES↗
DOE OSTI2020

Deep Ensemble Confidence Levels for Multi-hot Categorization

NOICE (Neural Optical Image Categorizer for the Elog) is a small collaboration tasked with categorizing the images in the Fermilab Accelerator Division electronic logbook by using Artificial Intelligence. To do so, we manually categorized a subset of the images in the E-log into nine independent labels. Each image was then multi-hot-encoded into a nine-dimensional binary vector because each image could have more then one label.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms [Slides]

Deep learning is used in many applications in the physical sciences. In those sciences we are used to having uncertainty on every measurement or prediction. In the last years, many methods have been put forth for uncertainty quantification: Bayesian Neural Networks, Concrete Dropout, and Deep Ensembles. Uncertainty in deep learning is often divided into aleatoric or irreducible and epistemic or reducible. The problem remains: Which uncertainty quantification method should be chosen? How are those results interpreted?

97 MATHEMATICS AND COMPUTING↗
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 OSTI2021

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Examples of Mission-driven Data Science from Jefferson Lab and ACES

This presentation details mission-driven data science initiatives at Jefferson Lab and the Joint Institute for Advanced Computing on Environmental Studies (ACES). JLab, a U.S. Department of Energy Office of Science national laboratory, operates the Continuous Electron Beam Accelerator Facility (CEBAF), and is the lead institute for the new High Performance Data Facility (HPDF) Hub. The Joint Institute for ACES brings together interdisciplinary teams in health informatics, climate modeling, computer science, and physics to address environmental challenges, including flood modeling. The Hampton Roads region, particularly Norfolk and Virginia Beach, faces increasing flood risks, motivating the need for rapid, reliable, and risk-aware decision support. ACES’s flooding work has a focus on uncertainty quantification (UQ) and machine learning (ML) for coastal flood management. The work is motivated by the increasing vulnerability of communities such as Norfolk and Virginia Beach, Virginia, to frequent coastal flooding events, and the need for rapid, reliable decision support. The research develops computationally efficient ML surrogate models to forecast water levels and flooding risk. A central theme is the quantification and calibration of predictive uncertainty, especially for out-of-distribution (OOD) scenarios, using techniques such as Monte Carlo Dropout, Deep Ensembles, Gaussian Processes, and Deep Quantile Regression (DQR). The study demonstrates that distance-aware UQ is critical for reliable scientific AI, particularly in high-dimensional, safety-critical, and real-time applications.

McSpadden, Diana [Thomas Jefferson National Accele↗
NASA NTRS2020

Ensemble-Based Deep Learning for Estimating PM2.5 over California with Multisource Big Data Including Wildfire Smoke

Estimating PM2.5 concentrations and their prediction uncertainties at a high spatiotemporal resolution is important for air pollution health effect studies. This is particularly challenging for California, which has high variability in natural (e.g. wildfires, dust) and anthropogenic emissions, meteorology, topography (e.g. desert surfaces, mountains, snow cover) and land use.

air quality↗