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All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Teaching a neural network to attach and detach electrons from molecules

Abstract Interatomic potentials derived with Machine Learning algorithms such as Deep-Neural Networks (DNNs), achieve the accuracy of high-fidelity quantum mechanical (QM) methods in areas traditionally dominated by empirical force fields and allow performing massive simulations. Most DNN potentials were parametrized for neutral molecules or closed-shell ions due to architectural limitations. In this work, we propose an improved machine learning framework for simulating open-shell anions and cations. We introduce the AIMNet-NSE (Neural Spin Equilibration) architecture, which can predict molecular energies for an arbitrary combination of molecular charge and spin multiplicity with errors of about 2–3 kcal/mol and spin-charges with error errors ~0.01e for small and medium-sized organic molecules, compared to the reference QM simulations. The AIMNet-NSE model allows to fully bypass QM calculations and derive the ionization potential, electron affinity, and conceptual Density Functional Theory quantities like electronegativity, hardness, and condensed Fukui functions. We show that these descriptors, along with learned atomic representations, could be used to model chemical reactivity through an example of regioselectivity in electrophilic aromatic substitution reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Deep Symbolic Optimization for Electric Component Sizing in Fixed Topology Power Converters

Power converters (PC) are a major component in any current electronic hardware device. The development and design is usually guided by expert knowledge and heavily relies on human intuition and experience. The process is a very time consuming and costly activity and it is generally hard to improve upon current designs. As a first step towards autonomous PC design, we are here proposing a new framework for the sizing of components for fixed topology PCs based on given design requirements. To this end, we developed surrogate models for rapid evaluation of new topologies and adapt the deep symbolic optimization (DSO) framework to generate new topologies guided by a reinforcement learning training signal. In an empirical evaluation, we show that our DSO based approach is able to find the optimal configuration for all investigated topologies, while reducing the learning time by at least a factor of 100 compared to popular RL algorithms.

Xue, Lincoln↗
NASA NTRS2022

Revisiting the Ground Magnetic Field Perturbations Challenge: A Machine Learning Perspective

Forecasting ground magnetic field perturbations has been a long-standing goal of the space weather community. The availability of ground magnetic field data and its potential to be used in geomagnetically induced current studies, such as risk assessment, have resulted in several forecasting efforts over the past few decades. One particular community effort was the Geospace Environment Modeling (GEM) challenge of ground magnetic field perturbations that evaluated the predictive capacity of several empirical and first principles models at both mid- and high-latitudes in order to choose an operative model. In this work, we use three different deep learning models-a feed-forward neural network, a long short-term memory recurrent network and a convolutional neural network-to forecast the horizontal component of the ground magnetic field rate of change (dB H /dt) over 6 different ground magnetometer stations and to compare as directly as possible with the original GEM challenge. We find that, in general, the models are able to perform at similar levels to those obtained in the original challenge, although the performance depends heavily on the particular storm being evaluated. We then discuss the limitations of such a comparison on the basis that the original challenge was not designed with machine learning algorithms in mind.

Victor A. Pinto↗
DOE OSTI2022

Training calibration-based counterfactual explainers for deep learning models in medical image analysis

The rapid adoption of artificial intelligence methods in healthcare is coupled with the critical need for techniques to rigorously introspect models and thereby ensure that they behave reliably. This has led to the design of explainable AI techniques that uncover the relationships between discernible data signatures and model predictions. In this context, counterfactual explanations that synthesize small, interpretable changes to a given query while producing desired changes in model predictions have become popular. This under-constrained, inverse problem is vulnerable to introducing irrelevant feature manipulations, particularly when the model’s predictions are not well-calibrated. Hence, in this paper, we propose the TraCE (training calibration-based explainers) technique, which utilizes a novel uncertainty-based interval calibration strategy for reliably synthesizing counterfactuals. Given the wide-spread adoption of machine-learned solutions in radiology, our study focuses on deep models used for identifying anomalies in chest X-ray images. Using rigorous empirical studies, we demonstrate the superiority of TraCE explanations over several state-of-the-art baseline approaches, in terms of several widely adopted evaluation metrics. Our findings show that TraCE can be used to obtain a holistic understanding of deep models by enabling progressive exploration of decision boundaries, to detect shortcuts, and to infer relationships between patient attributes and disease severity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Feature learning and generalization in deep networks with orthogonal weights

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

From RNNs to Foundation Models: An Empirical Study on Commercial Building Energy Consumption

Accurate short-term energy consumption forecasting for commercial buildings is crucial for smart grid operations. While smart meters and deep learning models enable forecasting using past data from multiple buildings, data heterogeneity from diverse buildings can reduce model performance. The impact of increasing dataset heterogeneity in time series forecasting, while keeping size and model constant, is understudied. We tackle this issue using the ComStock dataset, which provides synthetic energy consumption data for U.S. commercial buildings. Two curated subsets, identical in size and region but differing in building type diversity, are used to assess the performance of various time series forecasting models, including finetuned open-source foundation models (FMs). The results show that dataset heterogeneity and model architecture have a greater impact on post-training forecasting performance than the parameter count. Moreover, despite the higher computational cost, finetuned FMs demonstrate competitive performance compared to base models trained from scratch.

commercial buildings↗
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

Recurrent Convolutional Deep Neural Networks for Modeling Time-Resolved Wildfire Spread Behavior

The increasing incidence and severity of wildfires underscores the necessity of accurately predicting their behavior. While high-fidelity models derived from first principles offer physical accuracy, they are too computationally expensive for use in real-time fire response. Low-fidelity models sacrifice some physical accuracy and generalizability via the integration of empirical measurements, but enable real-time simulations for operational use in fire response. Machine learning techniques have demonstrated the ability to bridge these objectives by learning first-principles physics while achieving computational speedups. While deep learning approaches have demonstrated the ability to predict wildfire propagation over large time periods, time-resolved fire-spread predictions are needed for active fire management. Here, in this work, we evaluate the ability of deep learning approaches in accurately modeling the time-resolved dynamics of wildfires. We use an autoregressive process in which a convolutional recurrent deep learning model makes predictions that propagate a wildfire over 15 min increments. We apply the model to four simulated datasets of increasing complexity, containing both field fires with homogeneous fuel distribution as well as real-world topologies sampled from the California region of the United States. We show that even after 100 autoregressive predictions representing more than 24 h of simulated fire spread, the resulting models generate stable and realistic propagation dynamics, achieving a Jaccard score between 0.89 and 0.94 when predicting the resulting fire scar. The inference time of the deep learning models are examined and compared, and directions for future work are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2024

Celebrating 10 Years of the Sub-Seasonal to Seasonal Prediction Project and Looking to the Future

The conference clearly demonstrated the increasing interest and growth of the scientific community working on the development and application of sub-seasonal to seasonal prediction since the start of the World Weather Research Programme (WWRP)/World Climate Research Programme (WCRP) sub-seasonal to seasonal (S2S) prediction project in 2013. The conference, which was held at the University of Reading (United Kingdom), was organized into three main themes as briefly summarized below, with eleven invited talks, 74 oral contributed talks, and 101 posters. The conference also included a two-hour breakout session, wherein eight groups discussed the current state and prospect for S2S prediction, and an early career researcher event. A summary of these discussions and recommendations is presented below. The conference web page (https://research.reading.ac.uk/s2s-summit2023/) is archived at the University of Reading. Introductory comments by representatives of the World Meteorological Organization (WMO) WWRP and WCRP emphasized the importance of the weather–climate linkage, targeted by S2S forecasts (from 2 weeks to a season ahead), addressing the challenges of creating “end-to-end” forecasts that encompass the entire climate-services chain from the prediction science and forecast, to the development and issuing of forecast products tailored to informing user-decisions. They also emphasized the efficacy of multi-model ensemble efforts and databases to foster collaborations internationally and between operational centres and academia. Although the WWRP/WCRP S2S project comes to an end in 2023, S2S prediction will remain an important focus for WWRP and WCRP. In WWRP, a new project called SAGE (Sub-seasonal to seasonal predictions for Agriculture and Environment) will start in 2024. Another important legacy of the S2S project will be the maintenance of the S2S database (Vitart et al. 2017) and the establishment of a WMO Lead Center for sub-seasonal prediction multi-model ensemble (LC-SSPMME) which will provide real-time multi-model S2S climate information. In two keynote presentations, Prof. Brian Hoskins (University of Reading) and Dr. Gilbert Brunet (Australian Bureau of Meteorology) discussed the potential of S2S predictability and the ongoing journey for understanding and improving these predictions. This conference was a sequel to the International Conference on Sub-seasonal to Seasonal Prediction (Robertson et al., 2014) which took place in College Park (Maryland, USA) in February 2014 to celebrate the start of the WWRP/WCRP S2S project, and to WCRP and WWRP conferences in Boulder, USA, in 2018 (Merryfield et al., 2020). A significant development compared to the previous S2S conferences was the large number of presentations on research to operation (R2O) and S2S applications and on the use of artificial intelligence and machine learning (AI/ML) methods for S2S prediction. Some of these methods provide empirical S2S forecasts which are competitive with state-of-the-art dynamical models. Other presentations demonstrated that AI/ML can provide alternative calibration of dynamical model outputs to traditional methods. Several talks and posters highlighted the increasing use of AI/ML, including deep learning, in S2S forecast post-processing and using AI to identify higher flow-dependent skill. Finally, some presentations demonstrated the value of AI/ML methods for a better understanding of S2S sources of predictability and attribution of extreme events.

S. J. Woolnough↗
DOE OSTI2026

Deep nonparametric estimation of operators between infinite dimensional spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗
DOE OSTI2022

A Scalable Pipeline for Gigapixel Whole Slide Imaging Analysis on Leadership Class HPC Systems

Whole Slide Imaging (WSI) captures microscopic details of a patient's histopathological features at multiple res-olutions organized across different levels. Images produced by WSI are gigapixel-sized, and saving a single image in memory requires a few gigabytes which is scarce since a complicated model occupies tens of gigabytes. Performing a simple met-ric operation on these large images is also expensive. High-performance computing (HPC) can help us quickly analyze such large images using distributed training of complex deep learning models. One popular approach in analyzing these images is to divide a WSI image into smaller tiles (patches) and then train a simpler model with these reduced-sized but large numbers of patches. However, we need to solve three pre-processing challenges efficiently for pursuing this patch-based approach. 1) Creating small patches from a high-resolution image can result in a high number (hundreds of thousands per image) of patches. Storing and processing these images can be challenging due to a large number of I/O and arithmetic operations. To reduce I/Oand memory accesses, an optimal balance between the size and number of patches must exist to reduce I/O and memory accesses. 2) WSI images may have tiny annotated regions for cancer tissue and a significant portion with normal and fatty tissues; correct patch sampling should avoid dataset imbalance. 3) storing and retrieving many patches to and from disk storage might incur I/O latency while training a deep learning model. An efficient distributed data loader should reduce I/O latency during the training and inference steps. This paper explores these three challenges and provides empirical and algorithmic solutions deployed on the Summit supercomputer hosted at the Oak Ridge Leadership Computing Facility.

Dash, Sajal↗
DOE OSTI2022

Hybrid Quantum-Classical Neural Networks

Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers are soon expected to approach the physical limitations that will slow their performance improvements in the near future. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated IBM universal quantum computer and a state-of-the-art IBM universal quantum computer. On the simulated hardware, we observe that the hybrid neural network achieves around 10% higher classification accuracy and 20% better minimization of the cost function than an individual variational quantum circuit. On the quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.

Arthur, Davis↗
NASA NTRSDate not supplied

Hybrid Modeling for Complex Systems Health Management

The research work presents application of hybrid physics-informed machine learning to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage. The powertrain model consists of Li-ion batteries, electronic speed controller with pulse-width modulation, and brush-less DC motor with connected propeller. Results obtained from combination of laboratory and simulation tests are discussed in this work.

PINNS↗
NASA NTRSDate not supplied

Hybrid Modeling of Unmanned Aerial Vehicle Electric Powertrain for Fault Detection and Diagnostics

This paper shows the application of hybrid physics-informed machine learning to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived principles and empirical equations, as well as fully connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage. It has already been applied to Li-ion batteries in the past, and in this work, we extend the applications to other components of an electric powertrain, namely electronic speed controller with pulse-width modulation, and brushless DC motor with connected propeller. Training and testing of the model is carried out using experimental data from Li-ion battery discharge and powertrain testing in a laboratory environment.

Physics-Informed Machine Learning↗
DOE OSTI2025

Differential Seismic Phase Detection Probability as a Potential Discriminant of Explosions and Earthquakes

Deep learning models trained to estimate the probability of seismic P and S phases are rapidly expanding the scale of local event detections. Here, we evaluate the potential for deep learning model output phase detection probabilities to contribute to event‐type classification, particularly discrimination of single‐fired borehole explosions and earthquakes at local distances (<300 km). Motivated by the empirical success of P/S amplitude ratios, we consider the difference between P and S pick probability output from previously developed phase detection models, P prob −S prob ⁠, as a discriminant. Test data include M L ∼1–4 earthquakes and explosions observed by common seismographs in ten geologically diverse localities. Depending on the picking model and training data, binary classification using P prob −S prob with at least three stations can achieve approximately equivalent classification accuracy as P/S amplitude ratios without requiring any customization. Joint classification with P/S and P prob −S prob improves accuracy for most quality control scenarios. Pick probabilities are an efficient attribute to consider in explosion discrimination because they can be automated byproducts of event detection. They avoid the binary choice of picking or not picking weakly visible S waves common to explosions.

Duan, Chenglong [Rice Univ., Houston, TX (United S↗