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All sources NASA NTRS DOE OSTI

DOE OSTI2025

An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage (q C ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, q C , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The q C is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the c k -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by q C .

Bayesian data assimilation↗

DOE OSTI2020

Detection of atmospheric rivers with inline uncertainty quantification: TECA-BARD v1.0.1

It has become increasingly common for researchers to utilize methods that identify weather features in climate models. There is an increasing recognition that the uncertainty associated with choice of detection method may affect our scientific understanding. For example, results from the Atmospheric River Tracking Method Intercomparison Project (ARTMIP) indicate that there are a broad range of plausible atmospheric river (AR) detectors and that scientific results can depend on the algorithm used. There are similar examples from the literature on extratropical cyclones and tropical cyclones. It is therefore imperative to develop detection techniques that explicitly quantify the uncertainty associated with the detection of events. We seek to answer the following question: given a “plausible” AR detector, how does uncertainty in the detector quantitatively impact scientific results? We develop a large dataset of global AR counts, manually identified by a set of eight researchers with expertise in atmospheric science, which we use to constrain parameters in a novel AR detection method. We use a Bayesian framework to sample from the set of AR detector parameters that yield AR counts similar to the expert database of AR counts; this yields a set of “plausible” AR detectors from which we can assess quantitative uncertainty. This probabilistic AR detector has been implemented in the Toolkit for Extreme Climate Analysis (TECA), which allows for efficient processing of petabyte-scale datasets. We apply the TECA Bayesian AR Detector, TECA-BARD v1.0.1, to the MERRA-2 reanalysis and show that the sign of the correlation between global AR count and El Niño–Southern Oscillation depends on the set of parameters used.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches

Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.

Advanced reactors↗

DOE OSTI2024

Assay-based background projection for the Majorana Demonstrator using Monte Carlo uncertainty propagation

The background index (BI) is an important quantity to project and calculate the half-life sensitivity of neutrinoless double-𝛽 decay (0⁢𝜈⁢𝛽⁢𝛽) experiments. An analysis framework is presented to calculate the BI using the specific activities, masses, and simulated efficiencies of an experiments components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a BI distribution from the specific activity, mass, and efficiency distributions. This method is applied to the M AJORANA D EMONSTRATOR , which deployed arrays of high-purity Ge detectors enriched in 76 Ge to search for 0⁢𝜈⁢𝛽⁢𝛽. The original assay-based projection is requantified in the new framework, using the as-built geometry of the Demonstrator and additional assay information. While 47% higher than the original projection, the resulting BI of [8.95±0.36]×10 −4 cts/(keVkgyr) from the 232 Th and 238 U decay chains does not account for the higher-than-expected BI observed by the D EMONSTRATOR . Finally, this method enables us to demonstrate the statistical incompatibility between the D EMONSTRATOR 's observed background and the assay results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Accurate and Timely Forecasts of Geologic Carbon Storage using Machine Learning Methods

Carbon capture and storage is one strategy to reduce greenhouse gas emissions. One approach to storing the captured CO2 is to inject it into deep saline aquifers. However, dynamics of the injected CO2 plume is uncertain and the potential for leakage back to the atmosphere must be assessed. Thus, accurate and timely forecasts of CO2 storage via real-time measurements integration becomes very crucial. This study proposes a learning-based, inverse-free prediction method that can accurately and rapidly forecast CO2 movement and distribution with uncertainty quantification based on limited simulation and observation data. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO2 storage site operators with an effective tool for real-time decision making.

Lu, Dan↗

NASA NTRS2007

Bayesian Analysis of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.

methods - statistical↗

DOE OSTI2023

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2022

Simulation and Application of Bayesian Dose Uncertainty Modeling for Low-Boom Community Noise Surveys

In dose-response modeling, failing to account for dose uncertainty can cause artificial flattening of the estimated slope of the dose-response curve. Previous analyses of NASA sonic boom community noise survey data utilized a Bayesian multilevel logistic regression model, which did not account for dose uncertainty. The current work extends the model to account for either classical or Berkson dose uncertainty. The extended model is applied to two simulated dose-response datasets to illustrate conditions under which the dose uncertainty term does and does not correct for the artificial flattening introduced by dose uncertainty. Finally, the extended model is applied to two previous NASA sonic boom community noise surveys. The resulting dose-response curve slope for the average participant is 5 to 10% steeper, but the difference in the noise dose that elicits a 5% highly annoyed response is small (less than 1 dB). The difference remains insignificant when producing population summary dose-response curves. Commentary is included on applicability to future X-59 low-boom community noise survey data modeling and analysis.

X-59↗

DOE OSTI2022

Reduced scale stripline platform to extend accessible pressures on the Z machine: Shockless compression of platinum to 650 GPa

Reaching astrophysically relevant high energy density (HED) material states in the laboratory is an ongoing effort at multiple experimental facilities. We have developed a new dynamic compression platform for the Z Pulsed Power Facility that allows for sample sizes 100s of [Formula: see text]m in thickness that accommodate multiple grains in order to fully capture bulk properties, such as material strength. A pair of experiments compressed platinum (Pt) to HED conditions and conventional inverse Lagrangian analysis as well as a recent Bayesian calibration technique were used to determine the principal isentrope to 650 GPa with density uncertainties of <2%. These low uncertainties are calculated for single sample experiments, presenting the possibility of even smaller experimental uncertainties with multiple samples the platform allows. Our new platform extends the accessible Pt ramp pressures achievable on the Z machine to over 80% of the pressure recently achieved using the National Ignition Facility planar Hohlraum platform. This new capability, the next generation evolution of the stripline platform, was made possible by advancements in both our understanding of the Z pulsed power driver and our overall magnetohydrodynamic modeling capabilities.

Porwitzky, Andrew↗

DOE OSTI2022

Baycal

Bayesian Model Calibration (BayCal) toolkit is a software plugin for Risk Analysis Virtual Environment (RAVEN) framework, arming at inversely quantifying the uncertainties associated with simulation model parameters based on available experiment data. BayCal seeks statistical inference of the uncertain input parameters that are consistent with the available measurement data or observed data. The unique feature of BayCal is the capability to be linked with RAVEN to build corresponding calibration workflows for complex multi-physics simulations. In addition to be able to use the machine learning capability of RAVEN to significantly reduce the computational cost of expensive simulation models, another distinctive feature of BayCal is the capability to deal with high-dimensional correlated model outputs, such as time series observations at multiple locations, via principal component analysis (PCA) technique.

Wang, Congjian↗

DOE OSTI2025

Elastic Bayesian Model Calibration

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Bayesian inference for plasmonic nanometrology

Here, we introduce a Bayesian method for the characterization of plasmonic nanoparticles, which is applicable to both near- and far-field problems. Designed to combine data generated from any photon-plasmon interaction experiment with physically motivated theoretical models, our approach leverages state-of-the-art Markov chain Monte Carlo sampling techniques and returns parameter estimates on nanometric scales. Simulated spectral data sets, describing resonant scattering of photons from ellipsoidal and toroidal nanoparticles, are explored as concrete examples of our approach, with the resulting Bayesian estimates showing excellent agreement with the ground truth, even under conditions of high statistical noise. By incorporating Bayes factors into the method as well, we reveal how model selection can determine which one of competing geometric shapes better explains the observed data. Our comprehensive nanometrology procedure can be tailored to a variety of light-particle interaction models, and its reliance on Bayesian inference furnishes automatic uncertainty quantification. In addition to applicability to a host of plasmonic configurations such as nanoparticle dimers, trimers, and array studies, it is proposed that the presented analysis can be extended to the quantum regime, where nonclassical photon statistics may provide additional insight for inference of scatterer properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Quantifying uncertainty in Pareto estimates of global lake area

Abstract Size is a critical factor determining the rate and occurrence of specific lake processes such as carbon sequestration and greenhouse gas emissions and emerging evidence suggests that small lakes in particular have particularly large CO 2 flux rates. Because we do not have a complete census of all lakes, upscaling estimates of such processes to small lakes at broad spatial scales requires the use of lake size‐abundance distributions rather than empirical measurements of area. Existing lake census efforts are incomplete such that as lakes become smaller, they are more likely to be omitted either because they are too small to be resolved from remote sensing products or because of limited ground surveying effort (i.e., “censoring” of small lakes relative to large lakes). The present study explores one potential shortcoming of prior approaches estimating global lake area using lake size‐abundance distributions. Namely, that these prior approaches rely on frequentist curve fitting techniques combined with an ad‐hoc cutoff determination strategy (visual inspection to determine a likely censoring point). This yields an over‐exact lake area estimate that is typically reported with no uncertainty bounds. I show how these shortcomings can be addressed with a Bayesian model that produces larger estimates of lake area uncertainty relative to the typical approach. When used as part of a sensitivity analysis, such an approach has the potential to enable more robust intercomparisons among studies of aquatic processes upscaling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

42 ENGINEERING↗

DOE OSTI2021

Analysis and Optimization of Seismo-Acoustic Monitoring Networks with Bayesian Optimal Experimental Design

The Bayesian optimal experimental design (OED) problem seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty. The goal of OED is to find an experiment that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge about expected data. Therefore, within the context of seismic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize the ability to locate seismic events from arrival time data of detected seismic phases. In order to do utilize Bayesian OED we must develop four elements:1. A likelihood function that describes the uncertainty of detection and travel times; 2. A Bayesian solver that takes a prior and likelihood to identify the posterior; 3. An algorithm to compute EIG; and, 4. An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we can explore many relevant questions to monitoring such as: how and what multiphenomenology data can be used to optimally reduce uncertainty, how to trade off sensor fidelity and earth model uncertainty, and how sensor types, number, and locations influence uncertainty

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Impact of multiplicity fluctuations on entropy scaling across system size

The initial state is one of the greatest uncertainties in heavy-ion collisions. A model-agnostic approach is taken in the phenomenological Trento framework which constrains parameters using Bayesian analysis. However, the color-glass condensate (CGC) effective theory predicts initial energy densities that lie outside the recent Bayesian analyses due, in part, to the assumption in Trento of event-by-event multiplicity fluctuations following a Γ distribution. We compare the Trento-preferred √T A T B scaling to CGC-like T A T B scaling coupled with log-normal fluctuations in AuAu and dAu collisions and find there is a significant impact on the multiplicity distributions and on the eccentricities, which may affect the extraction of viscosity in small systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Atikokan Digital Twin: Machine learning in a biomass energy system

The Atikokan Generating Station, operated by Ontario Power Generation, has a 200 MW, biomass-fired tower boiler that operates on a dispatch schedule with a five-minute cycle. The boiler is generally operated in the range of 40–100 MW using two of five burner levels. In order to optimize boiler performance, we propose the implementation of a unique digital twin. Our digital twin abstraction couples Bayesian inference from science-based models and from observations (machine learning) with decision theory to predict operating-variable set points that optimize the physical asset (the boiler) in the presence of uncertainty (artificial intelligence). We focus this paper on the continuous Bayesian machine learning part of the Atikokan Digital Twin; we discuss decision theory in a companion paper. We identify and learn about 12 operational, model, and measured-output parameters and their uncertainties from high-fidelity, science-based simulations of the Atikokan boiler and from the observed measurements at the power plant. Since the goal of the Atikokan Digital Twin is to implement it online in real time, we require fast function evaluations for the quantities of interest extracted from the simulations in the Bayesian analysis. We use Gaussian process regression/interpolation to create accurate, robust surrogate models. We define the Bayesian priors and likelihood function and solve for the posterior distributions of the 12 parameters. Here we then propagate these distributions (i.e., parameters with uncertainty) into the predicted distributions of 790 quantities of interest to learn about the relative importance of various sources of error including experimental, model, and operating-parameter errors.

09 BIOMASS FUELS↗

DOE OSTI2022

BayesMT: A Probabilistic Bayesian Framework for the Seismic Moment Tensor

Moment tensors (MTs) have long been used in earthquake and explosion source analysis, and there has been a renewed interest in how they can inform us about the seismic source, particularly in the geophysical monitoring community due to its application in event identification and yield analysis. However, parameter uncertainties in seismic MT inversion are rarely available. The inverse procedure often does not quantify MT model errors such as event location, data noise and Earth model that are essential for estimating solution robustness. To address this need, we propose to adopt the Bayesian probabilistic framework to incorporate uncertainties in MT inversions. In this study, we present the theoretical background of a probabilistic Bayesian framework for MT inversion accounting for model and measurements errors and illustrate the implementation of the method using a synthetic example.

58 GEOSCIENCES↗