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DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

DOE OSTI2024

Democratizing uncertainty quantification

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.

Benchmarks↗

DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗

DOE OSTI2025

The tensor-train stochastic finite volume method for uncertainty quantification

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Bayesian automated weighting of aggregated DFT, MD, and experimental data for candidate thermodynamic models of aluminum with uncertainty quantification

Atomic-scale modeling methods such as density functional theory (DFT) and molecular dynamics (MD) can predict the thermodynamic properties of materials at a lower cost than experimental measurements. However, their regular usage in thermodynamic model construction is hampered by the lack of quantitative agreement with experimental measurements and the lack of uncertainty estimates on the data. To make regular usage of this atomistic simulation data, it is important to assess whether the atomistic simulation datasets, by themselves or in combination with experimental measurements, result in the same physics-informed models best supported by experimental measurements alone. Here, models of aluminum thermodynamic properties are discussed using three data sources: atomistic calculations (DFT and MD), experiments, and a combination of atomistic calculations and experiments. The study shows that, after ensuring self-consistency in predicting key invariant points, both experimental measurements and atomistic calculations can significantly contribute to an optimal model.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Effects of grain size and porosity on cladding failure in high-burnup UO 2 : A sensitivity and uncertainty study

Isotopic taggants are being studied to aid in the provenance assessment of nuclear materials. However, these taggants must be selected such that they do not adversely affect fuel performance during normal operation or accident scenarios. Taggants are known to affect the fuel’s grain size and porosity. In the work described in this paper, the BISON fuel performance code was used to assess the potential effects of taggants (i.e., grain size and porosity) on fuel rod behavior and cladding failure during a high-burnup, large-break loss-of-coolant accident. Here, 281 individual fuel rods from the same reactor core were modeled for a sensitivity study, a parametric study, and uncertainty quantification. The cladding failure predictions often exhibited stochastic behavior. After additional study, it was found that the cladding failure model is highly sensitive to residual error inherent to numerical approximation solvers. Some strategies to mitigate this sensitivity are discussed. The study found no relationship between known taggant effects and cladding failure status. However, taggants were found to affect the time and location of failure in certain rods. In conclusion, future work to continue investigating and validating these findings is briefly discussed.

Doped UO 2↗

DOE OSTI2021

A probability density function model describing height estimation uncertainty due to image pixel intensity noise in digital fringe projection measurements

Digital fringe projection is a surface-profiling technique used for highly accurate non-contact measurements. As with any measurement technique, a variety of sources degrade to the measurement accuracy of the method. Here, this paper presents an analytically-derived probability density function that explicitly models the surface height measurement error due to inevitable phase measurement error, and it includes the specific case of pixel noise inducing the phase measurement error that ultimately leads to the height estimation error. The accuracy of the model was validated through Monte-Carlo simulations of resultant height distributions subject to arbitrarily correlated pixel intensity noise and experimental digital fringe projection measurements where the pixel-by-pixel height uncertainty estimations were compared to the predictions of the derived model.

42 ENGINEERING↗

DOE OSTI2024

Characterizing model uncertainties in simulated coast-to-offshore wind over the northeast U.S. using multi-platform measurements from the TCAP field campaign

Numerical weather prediction (NWP) models, such as the Weather Research and Forecasting (WRF) model, are widely used to provide estimates of the offshore wind energy resource owing to their large spatial coverage compared to available observations. Nevertheless, spatiotemporal distribution of model biases is highly dependent on factors including model configuration, location, and the interplay of multi-scale physical processes. Here, in this study, we focus on the characterization of model uncertainties in simulated coast-to-offshore winds over the northeast U.S., by varying sea surface temperature (SST) forcings, surface layer (SL) and planetary boundary layer (PBL) parameterizations, as well as identifying biases that may be directly passed from initial and boundary conditions. Multiple measurements, including aircraft data collected during the U.S. Department of Energy's Two-Column Aerosol Project (TCAP) experiment, are used to constrain the model results and facilitate quantitative comparisons. Our analysis indicates while SST forcing has notable impacts on simulated air temperature and moisture within PBL, the modeled winds are in general more sensitive to the choices of SL and PBL physics than to SST. The model’s forcing data not only controls the vertical dependence of wind speed errors, but also alters regional variability in wind speed’s spatial correlation. Bias comparisons between ERA5 reanalysis and ensemble simulations revealed significant similarity, particularly in wind speed biases during winter, underscoring their dependency on initial and boundary conditions. Coastal and offshore near-surface wind speed biases tend to exhibit much higher similarity in winter than in summer due to the presence of much stronger and more persistent synoptic wind conditions. This study highlights the importance of accurate atmospheric forcing and parameterization choices in improving wind forecasts and suggests the potential for extrapolating coastal wind biases to offshore locations, aiding wind energy forecasting and informing the Wind Forecast Improvement Project-3 (WFIP3).

17 WIND ENERGY↗

DOE OSTI2021

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual link failure after some amount of elapsed time. The descriptor loss of assured safety (LOAS) is used because failure of the WL system places the entire system in an inoperable configuration while failure of the SL system before failure of the WL system, although undesirable, does not necessarily result in an unintended operation of the entire system. Thus, safety is “assured” by failure of the WL system before failure of the SL system. Here, the following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation, approximation and illustration of PLOAS with (a) constant delay times, (b) aleatory uncertainty in delay times, and (c) delay times defined by functions of link properties at occurrence times for link failure precursors, and (iii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

58 GEOSCIENCES↗

DOE OSTI2023

UQpy v4.1: Uncertainty quantification with Python

This paper presents the latest improvements introduced in Version 4 of the UQpy, Uncertainty Quantification with Python, library. In the latest version, the code was restructured to conform with the latest Python coding conventions, refactored to simplify previous tightly coupled features, and improve its extensibility and modularity. To improve the robustness of UQpy, software engineering best practices were adopted. A new software development workflow significantly improved collaboration between team members, and continuous integration and automated testing ensured the robustness and reliability of software performance. Continuous deployment of UQpy allowed its automated packaging and distribution in system agnostic format via multiple channels, while a Docker image enables the use of the toolbox regardless of operating system limitations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

UQpy Version 4.2: Uncertainty quantification with Python

We introduce a new module for the UQpy software package which extends its capabilities into the field of Scientific Machine Learning. This module builds on PyTorch to create a flexible and robust platform for uncertainty quantification in machine learning. The scientific machine learning module of UQpy introduces custom layers, neural networks, and neural network trainers that are compatible with torch version 2.2.2 and allow for “plug and play” integration into existing torch code.

Neural networks↗

DOE OSTI2021

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol –1 , and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗

DOE OSTI2024

Data Imbalance, Uncertainty Quantification, and Transfer Learning in Data‐Driven Parameterizations: Lessons From the Emulation of Gravity Wave Momentum Transport in WACCM

Abstract Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO 2 ). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Bounding uncertainty in functional data: A case study

Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Effects of ionising radiation exposure in offspring and next generations: dosimetric aspects and uncertainties

The impact of the exposure to ionizing radiation in the offspring and next generation has been investigated in the last decades and currently is the subject of study of the ICRP Task Group 121. Studying the effects of radiation exposure in pre-conceptional and post-conceptional phases can be a challenge since potential effects to the fetus vary depending on the stage of fetal development. Epidemiology and radiobiology studies are the two sources of information one can use to correlate the radiation dose to the human body and tissues and the resulting effects. For a proper evaluation of the outcomes of such studies, and a correct appraisal of the exposure/dose-effect relationship, (i) reliable dosimetry, (ii) accurate reporting, and (iii) reproducibility of results are required. Although variables related to dose, including for instance source of radiation, geometry of irradiation, dose rate etc., are usually known, especially in radiobiology studies, often important details of the irradiation are not reported. In conclusion, based on standards developed by the National Cancer Institute (NCI), the National Institute of Allergy and Infectious Disease (NIAID) and the National Institute of Standards and Technology (NIST), a review of the scientific studies used by the UNSCEAR to estimate the risk of hereditary effects, and by the ICRP in its current recommendations, was conducted to evaluate the way dosimetry was reported. Dosimetry and the related uncertainties were not adequately described in the vast majority of those studies. This does not necessarily mean that they do not provide relevant information, however it prevents from a thorough verification and reproduction of their findings. In order to guarantee the reliability and robustness of the process of revision of the estimates of risk and detriment it is therefore considered mandatory to include a careful check of the new relevant literature with regard to the criteria on the completeness and reproducibility of the dosimetric information.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

DOE OSTI2021

Get on the BAND Wagon: a Bayesian framework for quantifying model uncertainties in nuclear dynamics

In this paper, we describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Distance preserving machine learning for uncertainty aware accelerator capacitance predictions

Abstract Accurate uncertainty estimations are essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold standard for this task; however, they can struggle with large, high-dimensional datasets. Combining deep neural networks with Gaussian process approximation techniques has shown promising results, but dimensionality reduction through standard deep neural network layers is not guaranteed to maintain the distance information necessary for Gaussian process models. We build on previous work by comparing the use of the singular value decomposition against a spectral-normalized dense layer as a feature extractor for a deep neural Gaussian process approximation model and apply it to a capacitance prediction problem for the High Voltage Converter Modulators in the Oak Ridge Spallation Neutron Source. Our model shows improved distance preservation and predicts in-distribution capacitance values with less than 1% error.

43 PARTICLE ACCELERATORS↗