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DOE OSTI2025

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part IV: PFNS and $\bar{ν}$ Uncertainty Propagation

An analytic benchmark with continuous-energy cross sections was previously derived to validate criticality calculations. Here, to extend the utility of the analytic benchmark to verify the implementation of $\bar{ν}$ and prompt fission neutron spectrum (PFNS) uncertainty propagation methods, new simplified forms that are dependent on the incident (fission-causing) neutron energy, as well as the outgoing neutron energy for the PFNS, are introduced in this work. The analytical forms for the flux and adjoint flux are derived for the extended benchmark and used to determine the 𝑘-eigenvalue sensitivity to $\bar{ν}$ and PFNS. The 𝑘-eigenvalue uncertainty due to $\bar{ν}$ and PFNS is calculated for the analytic benchmark using simplified$\bar{ν}$ and PFNS representations based on the ENDF-B/VIII.0 239 Pu evaluation. Because of the low sensitivity of the analytic benchmark to the physical PFNS, a nonphysical high-sensitivity PFNS is also presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Uncertainty propagation in pore water chemical composition calculation using surrogate models

Performance assessment in deep geological nuclear waste repository systems necessitates an extended knowledge of the pore water chemical conditions prevailing in host-rock formations. In the last two decades, important progress has been made in the experimental characterization and thermodynamic modeling of pore water speciation, but the influence of experimental artifacts and uncertainties of thermodynamic input parameters are seldom evaluated. In this respect, we conducted an uncertainty propagation study in a reference geochemical model describing the pore water chemistry of the Callovian-Oxfordian clay formation. Nineteen model input parameters were perturbed, including those associated to experimental characterization (leached anions, exchanged cations, cation exchange selectivity coefficients) and those associated to generic thermodynamic databases (solubilities). A set of 13 quantities of interest were studied by the use of polynomial chaos expansions built non-intrusively with a least-squares forward stepwise regression approach. Training and validation sets of simulations were carried out using the geochemical speciation code PHREEQC. The statistical results explored the marginal distribution of each quantity of interest, their bivariate correlations as well as their global sensitivity indices. The influence of the assumed distributions for input parameters uncertainties was evaluated by considering two parametric domain sizes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Development and application of two-step uncertainty propagation and sensitivity analysis methodology for fast reactor safety analysis

Uncertainty quantification (UQ) in nuclear reactors for transients is directly linked with safety assessment through the cross-sections uncertainties, provided as a covariance matrix, which are propagated through the reactor system to output of interest pertaining to reactor safety, such as peak temperatures in fuel/clad/coolant. Using a two-step approach, uncertainties are first quantified and propagated from basic input variables (such as reaction cross-sections) to intermediate quantities (such as reactivity feedback coefficients) through lattice level calculations. Uncertainties of intermediate quantities (from the first step) are then propagated through the system transient calculations, in the second step, to obtain uncertainties on reactor safety output parameters of interest. The scope of this work consists of Uncertainty Quantification & Propagation of nuclear data uncertainties that are highly correlated through unprotected transient overpower and unprotected loss of flow to assess their impact on core safety parameters. This two-step approach in the presence of covariance renders the sensitivity analysis very challenging. In fact, usually the sensitivity analysis is restricted to each step, which limits its application since the sensitivities between the system output quantities and the basic input variables are difficult to obtain. Here, in this work, we address this issue by proposing a simple, general methodology to combine the sensitivity indices obtained in each step by assuming the model behavior being linear. For the first step Generalized Perturbation theory based indices are used while in the second step the recently studied Johnson indices. The uncertainty quantification and sensitivity methodologies discussed here are demonstrated on a generic LFR design which is based on the 500 MWth demonstration Lead-cooled fast reactor (DLFR) using oxide fuel, developed by Westinghouse Electric Company (WEC).

42 - ENGINEERING↗

DOE OSTI2024

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Uncertainty Propagation within Chained Models for Machine Learning Reconstruction of Neutrino-LAr Interactions

Sequential or chained models are increasingly prevalent in machine learning for scientific applications, due to their flexibility and ease of development. Chained models are particularly useful when a task is separable into distinct steps with a hierarchy of meaningful intermediate representations. In reliability-critical tasks, it is important to quantify the confidence of model inferences. However, chained models pose an additional challenge for uncertainty quantification, especially when input uncertainties need to be propagated. In such cases, a fully uncertainty-aware chain of models is required, where each step accepts a probability distribution over the input space, and produces a probability distribution over the output space. In this work, we present a case study for adapting a single model within an existing chain, designed for reconstruction within neutrino-Argon interactions, developed for neutrino oscillation experiments such as MicroBooNE, ICARUS, and the future DUNE experiment. We test the performance of an input uncertainty-enabled model against an uncertainty-blinded model using a method for generating synthetic noise. By comparing these two, we assess the increase in inference quality achieved by exposing models to upstream uncertainty estimates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Uncertainty Propagation from Experiment Measurements to Modeling Approaches: A Case for SMR Steam Entrainment Testing

To license new and advanced reactor designs, regulators must be convinced that their unique safety cases—relative to existing large scale reactors—have been adequately addressed by the designed reactor protection systems. In water cooled small modular reactors (SMRs), droplet entrainment in steam flow has significant implications on the progression of accident scenarios due to its compact design features, which requires representative test data applicable to SMR designs. Computer code, modeling and simulation (M&S) tools and models require adequate verification, assessment, and qualification. This includes M&S results validation against scaled empirical data within allowable uncertainty bands to gain regulatory approvals during the various stages of reactor system design, demonstration, and commercialization. However, measurement uncertainty within the empirical datasets and test data applicability ranges requires careful consideration of M&S inputs (i.e., boundary conditions, and initial conditions), and verification and validation efforts. This study focuses on uncertainty quantification in designing scaled test facilities for SMR applications with appropriate measurements and a standard data-reduction method to estimate thermal hydraulics characteristics parameters that incorporate physics phenomena of interest. In addition, this study supports the evaluation model development and assessment process using M&S that interfaces with advanced computing tools and digital twin capabilities. This will allow synchronization between experiment and modeling approaches for droplet entrainment testing and analysis, improving diagnostics, prognostics, and decision-making to accelerate regulatory approval.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020