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Results for “Uncertainty quantification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,765 records · Page 98
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Sequential experimental design based generalised ANOVA

Over the last decade, surrogate modelling technique has gained wide popularity in the field of uncertainty quantification, optimization, model exploration and sensitivity analysis. This approach relies on experimental design to generate training points and regression/interpolation for generating the surrogate. In this work, it is argued that conventional experimental design may render a surrogate model inefficient. In order to address this issue, this paper presents a novel distribution adaptive sequential experimental design (DA-SED). The proposed DA-SED has been coupled with a variant of generalised analysis of variance (G-ANOVA), developed by representing the component function using the generalised polynomial chaos expansion. Moreover, generalised analytical expressions for calculating the first two statistical moments of the response, which are utilized in predicting the probability of failure, have also been developed. The proposed approach has been utilized in predicting probability of failure of three structural mechanics problems. It is observed that the proposed approach yields accurate and computationally efficient estimate of the failure probability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Data-driven probability concentration and sampling on manifold

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Polynomial chaos representation of databases on manifolds

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Nested polynomial trends for the improvement of Gaussian process-based predictors

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation

We introduce an efficient non-intrusive surrogate-based methodology for global sensitivity analysis and uncertainty quantification. Modified covariance-based sensitivity indices (mCov-SI) are defined for outputs that reflect correlated effects. The overall approach is applied to simulations of a complex plasma-coupled combustion system with disparate uncertain parameters in sub-models for chemical kinetics and a laser-induced breakdown ignition seed. The surrogate is based on an Analysis of Variance (ANOVA) expansion, such as widely used in statistics, with orthogonal polynomials representing the ANOVA subspaces and a polynomial dimensional decomposition (PDD) representing its multi-dimensional components. The coefficients of the PDD expansion are obtained using a least-squares regression, which both avoids the direct computation of high-dimensional integrals and affords an attractive flexibility in choosing sampling points. This facilitates importance sampling using a Bayesian calibrated posterior distribution, which is fast and thus particularly advantageous in common practical cases, such as our large-scale demonstration, for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense. Effort, instead, is focused on efficient finite-resolution sampling. Standard covariance-based sensitivity indices (Cov-SI) are employed to account for correlation of the uncertain parameters. Magnitude of Cov-SI is unfortunately unbounded, which can produce extremely large indices that limit their utility. Alternatively, mCov-SI are then proposed in order to bound this magnitude $\in$ [0, 1]. The polynomial expansion is coupled with an adaptive ANOVA strategy to provide an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational cost of a high-dimensional expansion. It is also adaptively simplified according to the relative contribution of the different polynomials to the total variance. Finally, the approach is demonstrated for a laser-induced turbulent combustion simulation model, which includes parameters with correlated effects.

42 ENGINEERING↗
DOE OSTI2019

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A high-throughput approach for statistical process optimization in Laser Powder Bed Fusion

Process variability is inherent in metal additive manufacturing (AM). However, it is often overlooked in process optimization frameworks, constraining the understanding of process uncertainties and their influence on parameter selection. To address this, we present an integrated framework that combines high-throughput single-track experiments, GAN-based melt pool geometry extraction, robust statistical and machine learning modeling, and uncertainty-quantified process mapping. Process variability is characterized through single-track melt pool behaviors, and its influence on defect formation is systematically quantified to enable statistically guided process parameter optimization. This approach is demonstrated on Laser Powder Bed Fusion (L-PBF) of stainless steel 316L, effectively capturing the interplay between process parameters, melt pool variability, and defect probability. By integrating uncertainty quantification into process optimization, this study provides a structured methodology for addressing variability challenges in AM quality control, ultimately contributing to enhanced manufacturing reliability.

Laser Powder Bed Fusion↗
DOE OSTI2021

Improvement of the $\mathrm{BISON U_3Si_2}$ modeling capabilities based on multiscale developments to modeling fission gas behavior

Uranium silicide (U 3 Si 2 ) is a concept explored as a potential alternative to UO 2 fuel used in light water reactors (LWRs) since it may improve accident tolerance and economics due to its higher thermal conductivity and increased uranium density. U 3 Si 2 has been previously used in research reactors in the form of dispersion fuel, but operated at lower temperatures than commercial LWRs. The research reactor data illustrated that significant gaseous swelling occurs as the fuel burnup increases. Therefore, it is imperative to understand the fission gas behavior of U 3 Si 2 under higher temperature LWR operating conditions. In this work, molecular dynamics and phase-field modeling techniques are used to reduce the uncertainty in select modeling assumptions made in developing the fission gas behavior model for U 3 Si 2 in the BISON fuel performance code. These lower length scale informed models are then utilized in the validation of BISON U 3 Si 2 modeling capabilities to simulate the ATF-1 experiments irradiated in the Advanced Test Reactor (ATR). Sensitivity analysis (SA) and uncertainty quantification (UQ) are included as part of the validation process to identify where further experiments and lower length scale modeling would be beneficial. Here, the multiscale modeling approach utilized in this work can be applied to new fuel concepts being explored for both LWRs and advanced reactors (e.g., uranium nitride, uranium carbide).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Mobility assessment of the BCC and carbide phases in the C-Nb, C-U and Nb-U systems

Uranium carbides with refractory metal additions are considered for Gen IV nuclear reactors and nuclear thermal propulsion as fuels for their high-temperature and corrosion resistant properties. Understanding kinetic effects that dictate microstructural evolution during fabrication and operating conditions is essential to advance technological development of these fuels. This work presents the development of an atomic mobility database for C-Nb-U systems based off available experimental data supported with ab-initio methods. The mobility assessments and uncertainty quantification (using Markov chain Monte Carlo) were conducted in the Kawin software. Carbon diffusion is considered dominant, as metal diffusion is much slower, with niobium diffusion being even slower and rate limiting than uranium metal. We provide a comprehensive and self-consistent thermo-kinetic database that is validated by diffusion couple simulations through Kawin. In conclusion, this enables prediction of microstructural and phase evolution critical for the development and lifetime assessment of next generation nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Plutonium migration and phase evolution in irradiated U-Pu-Zr metallic fuels: An integrated EPMA-SEM-TEM study

Constituent redistribution is a defining feature of irradiated U-Pu-Zr metallic fuels, yet its mechanisms and effects on fuel performance are not sufficiently resolved to guide model development. Although decades of irradiation testing have established broad trends, a true mechanistic understanding of constituent redistribution has not been achieved. Here, in this study, we use electron probe microanalysis (EPMA), scanning electron microscopy (SEM), and transmission electron microscopy-based (TEM) selective area electron diffraction (SAED) on a EBR-II irradiated U-19 wt.% Pu-6 wt.% Zr fuel pin cross-section to correlate the composition, porosity, and crystallographic phases formed after irradiation. Constituent redistribution is thought to consist of three distinct zones, in which uranium and zirconium migrate while plutonium remains relatively unchanged. Our EPMA results resolve eight distinct compositional regions, and more importantly, show that plutonium redistributes alongside zirconium, contrary to historical assumptions. The distribution of fission products was highly asymmetric with a few large lanthanide precipitates observed at isolated sites on the pin periphery instead of a uniform distribution of smaller precipitates around the periphery. Using thermodynamic data from TAF-ID and the measured EPMA compositions, matrix phase fractions were predicted across the fuel radius. Phase predictions based on composition did not match TEM/SAED results, which revealed a much higher fraction of α−U phase than would be expected if phases were retained from reactor temperatures. These findings highlight the need for expanded SAED phase identification to capture post-irradiation and storage effects, as well as rigorous uncertainty quantification in fuel performance and phase diagram modeling to better constrain predictions from compositional data.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Documentation, assessment, and improvements of fission gas modeling capabilities in BISON

Fission gas behavior critically affects nuclear fuel performance, influencing thermal conductivity, microstructure, swelling, and fuel-cladding interactions. The Simple Integrated Fission Gas Release and Swelling (Sifgrs) model, implemented within the BISON fuel performance code, provides advanced capabilities for modeling these phenomena. This manuscript reviews and assesses Sifgrs’ modular structure and submodels describing intragranular, intergranular, and release mechanisms. The modular implementation enables rapid improvements as our understanding advances and new fuel forms emerge. After an overview of capabilities, we present a comprehensive validation suite, comparing predictions to experimental data from tests under normal and transient conditions, including reproduction of the Vitanza curve. Results demonstrate Sifgrs’ accuracy, robustness, and applicability. Current limitations and ongoing efforts are discussed, including mechanistic, multiscale modeling, uncertainty quantification, and validation within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, supporting the safe and efficient use of nuclear fuels.

BISON↗
DOE OSTI2023

A comparison of machine learning surrogate models of street-scale flooding in Norfolk, Virginia

Low-lying coastal cities, exemplified by Norfolk, Virginia, face the challenge of street flooding caused by rainfall and tides, which strain transportation and sewer systems and can lead to personal and property damage. While high-fidelity, physics-based simulations provide accurate predictions of urban pluvial flooding, their computational complexity renders them unsuitable for real-time applications. Using data from Norfolk rainfall events between 2016 and 2018, this study compares the performance of a previous surrogate model based on a random forest algorithm with two deep learning models: Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The comparison of deep learning to the random forest algorithm is motivated by the desire to utilize a machine learning architecture that allows for the future inclusion of common uncertainty quantification techniques and the effective integration of relevant, multi-modal features.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

FISPACT-II: An Advanced Simulation System for Activation, Transmutation and Material Modelling

Fispact-II is a code system and library database for modelling activation-transmutation processes, depletion-burn-up, time dependent inventory and radiation damage source terms caused by nuclear reactions and decays. The Fispact-II code, written in object-style Fortran, follows the evolution of material irradiated by neutrons, alphas, gammas, protons, or deuterons, and provides a wide range of derived radiological output quantities to satisfy most needs for nuclear applications. It can be used with any ENDF-compliant group library data for nuclear reactions, particle-induced and spontaneous fission yields, and radioactive decay (including but not limited to TENDL-2015, ENDF/B-VII.1, JEFF-3.2, JENDL-4.0u, CENDL-3.1 processed into fine-group-structure files, GEFY-5.2 and UKDD-16), as well as resolved and unresolved resonance range probability tables for self-shielding corrections and updated radiological hazard indices. The code has many novel features including: extension of the energy range up to 1 GeV; additional neutron physics including self-shielding effects, temperature dependence, thin and thick target yields; pathway analysis; and sensitivity and uncertainty quantification and propagation using full covariance data. The latest ENDF libraries such as TENDL encompass thousands of target isotopes. Nuclear data libraries for Fispact-II are prepared from these using processing codes PREPRO, NJOY and CALENDF. These data include resonance parameters, cross sections with covariances, probability tables in the resonance ranges, PKA spectra, kerma, dpa, gas and radionuclide production and energy-dependent fission yields, supplemented with all 27 decay types. All such data for the five most important incident particles are provided in evaluated data tables. The Fispact-II simulation software is described in detail in this paper, together with the nuclear data libraries. The Fispact-II system also includes several utility programs for code-use optimisation, visualisation and production of secondary radiological quantities. Included in the paper are summaries of results from the suite of verification and validation reports available with the code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

IAEA CIELO Evaluation of Neutron-induced Reactions on 235 U and 238 U Targets

Evaluations of nuclear reaction data for the major uranium isotopes 238 U and 235 U were performed within the scope of the CIELO Project on the initiative of the OECD/NEA Data Bank under Working Party on Evaluation Co-operation (WPEC) Subgroup 40 coordinated by the IAEA Nuclear Data Section. Both the mean values and covariances are evaluated from 10 -5 eV up to 30 MeV. The resonance parameters of 238 U and 235 U were re-evaluated with the addition of newly available data to the existing experimental database. The evaluations in the fast neutron range are based on nuclear model calculations with the code EMPIRE–3.2 Malta above the resonance range up to 30 MeV. 235 U(n,f), 238 U(n,f), and 238 U(n,γ) cross sections and 235 U(n th ,f) prompt fission neutron spectrum (PFNS) were evaluated within the Neutron Standards project and are representative of the experimental state-of-the-art measurements. The Standards cross sections were matched in model calculations as closely as possible to guarantee a good predictive power for cross sections of competing neutron scattering channels. 235 U(n,γ) cross section includes fluctuations observed in recent experiments. 235 U(n,f) PFNS for incident neutron energies from 500 keV to 20 MeV were measured at Los Alamos Chi-Nu facility and re-evaluated using all available experimental data. While respecting the measured differential data, several compensating errors in previous evaluations were identified and removed so that the performance in integral benchmarks was restored or improved. Covariance matrices for 235 U and 238 U cross sections, angular distributions, spectra and neutron multiplicities were evaluated using the GANDR system that combines experimental data with model uncertainties. Unrecognized systematic uncertainties were considered in the uncertainty quantification for fission and capture cross sections above the thermal range, and for neutron multiplicities. Evaluated files were extensively benchmarked to ensure good performance in reactor calculations and fusion-related systems. New comprehensive evaluations show excellent agreement with available differential data and integral performance better than current evaluated data libraries, and represent a step forward in a quest for better nuclear data for applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗