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DOE OSTI2013

Light Water Reactor Sustainability Program Support and Modeling for the Boiling Water Reactor Station Black Out Case Study Using RELAP and RAVEN

The existing fleet of nuclear power plants is in the process of extending its lifetime and increasing the power generated. In order to evaluate the impact of these two factors on the safety of the plant, the Risk Informed Safety Margin Characterization (RISMC) project aims to provide insight to decision makers through a series of simulations of the plant dynamics for different initial conditions (e.g., probabilistic analysis and uncertainty quantification). This report focuses, in particular, on the impact of power uprate on the safety of a boiled water reactor system. The case study considered is a loss of off-site power followed by the loss of diesel generators, i.e., a station black out (SBO) event. Analysis is performed by using a thermo-hydraulic code, i.e. RELAP-5, and a stochastic analysis tool currently under development at INL, i.e. RAVEN. Starting from the event tree models contained in SAPHIRE, we built the input file for RELAP-5 that models in great detail system dynamics under SBO conditions. We also interfaced RAVEN with RELAP-5 so that it would be possible to run multiple RELAP-5 simulation runs by changing specific keywords of the input file. We both employed classical statistical tools, i.e. Monte-Carlo, and more advanced machine learning based algorithms to perform uncertainty quantification in order to quantify changes in system performance and limitations as a consequence of power uprate. We also employed advanced data analysis and visualization tools that helped us to correlate simulation outcome such as maximum core temperature with a set of input uncertain parameters. Results obtained gave a detailed overview of the issues associated to power uprate for a SBO accident scenario. We were able to quantify how timing of safety related events were impacted by a higher reactor core power. Such insights can provide useful material to the decision makers to perform risk-infomed safety margins management.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗

DOE OSTI2025

MTUQ: a framework for estimating moment tensors, point forces, and their uncertainties

SUMMARY We introduce MTUQ, an open-source Python package for seismic source estimation and uncertainty quantification, emphasizing flexibility and operational scalability. MTUQ provides MPI-parallelized grid search and global optimization capabilities, compatibility with 1-D and 3-D Green’s function database formats, customizable data processing, C-accelerated waveform and first-motion polarity misfit functions, and utilities for plotting seismic waveforms and visualizing misfit and likelihood surfaces. Applicability to a range of full- and constrained-moment tensor, point force, and centroid inversion problems is possible via a documented application programming interface, accompanied by example scripts and integration tests. We demonstrate the software using three different types of seismic events: (1) a 2009 intraslab earthquake near Anchorage, Alaska; (2) an episode of the 2021 Barry Arm landslide in Alaska; and (3) the 2017 Democratic People’s Republic of Korea underground nuclear test. With these events, we illustrate the well-known complementary character of body waves, surface waves, and polarities for constraining source parameters. We also convey the distinct misfit patterns that arise from each individual data type, the importance of uncertainty quantification for detecting multimodal or otherwise poorly constrained solutions, and the software’s flexible, modular design.

58 GEOSCIENCES↗

DOE OSTI2014

ANALYSIS OF SAFETY IMPACTS FROM EXTERNAL FLOODING USING THE RISK-INFORMED SAFETY MARGIN CHARACTERIZATION (RISMC) TOOLKIT

The existing fleet of U.S. nuclear power plants is in the process of extending its lifetime and increasing the power generated from these plants via power uprates. In order to evaluate the impact of these factors on the safety of the plant, the Risk-Informed Safety Margin Characterization (RISMC) project aims to provide insight to decision makers through a series of simulations of the plant dynamics for different initial conditions (e.g., probabilistic analysis and uncertainty quantification). This paper demonstrates how Idaho National Laboratory (INL) researchers use the RISMC Toolkit to investigate complex nuclear plant phenomena using RAVEN and RELAP-7. The analysis focused on a highly relevant topic currently facing some nuclear power plants – specifically flooding issues. This research and development looked at challenges to a hypothetical pressurized water reactor, including: (1) a potential loss of off-site power followed by the possible loss of all diesel generators (i.e., a station black-out event), (2) earthquake induced station-blackout, and (3) a potential earthquake induced tsunami flood. The analysis is performed by using a set of codes: a thermal-hydraulic code (RELAP-7), a flooding simulation tool (NEUTRINO) and a stochastic analysis tool (RAVEN) – these are currently under development at INL. Using RAVEN, we were able to perform multiple RELAP-7 simulation runs by changing specific parts of the model in order to reflect specific aspects of different scenarios, including both the failure and recovery of critical components. The simulation employed traditional statistical tools (such as Monte-Carlo sampling) and more advanced machine-learning based algorithms to perform uncertainty quantification in order to understand changes in system performance and limitations as a consequence of power uprate. Qualitative and quantitative results obtained gave a detailed picture of the issues associated with potential accident scenarios. These types of insights can provide useful material for decision makers to perform risk-informed margins management.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Validation metrics for turbulent plasma transport

Developing accurate models of plasma dynamics is essential for confident predictive modeling of current and future fusion devices. In modern computer science and engineering, formal verification and validation processes are used to assess model accuracy and establish confidence in the predictive capabilities of a given model. This paper provides an overview of the key guiding principles and best practices for the development of validation metrics, illustrated using examples from investigations of turbulent transport in magnetically confined plasmas. Particular emphasis is given to the importance of uncertainty quantification and its inclusion within the metrics, and the need for utilizing synthetic diagnostics to enable quantitatively meaningful comparisons between simulation and experiment. As a starting point, the structure of commonly used global transport model metrics and their limitations is reviewed. An alternate approach is then presented, which focuses upon comparisons of predicted local fluxes, fluctuations, and equilibrium gradients against observation. The utility of metrics based upon these comparisons is demonstrated by applying them to gyrokinetic predictions of turbulent transport in a variety of discharges performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], as part of a multi-year transport model validation activity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Predictive Maturity of Multi-Scale Simulation Models for Fuel Performance

The project proposed to provide a Predictive Maturity Framework with its companion metrics that (1) introduce a formalized, quantitative means to communicate information between interested parties, (2) provide scientifically dependable means to claim completion of Validation and Uncertainty Quantification (VU) activities, and (3) guide the decision makers in the allocation of Nuclear Energy’s resources for code development and physical experiments. The project team proposed to develop this framework based on two complimentary criteria: (1) the extent of experimental evidence available for the calibration of simulation models and (2) the sophistication of the physics incorporated in simulation models. The proposed framework is capable of quantifying the interaction between the required number of physical experiments and degree of physics sophistication. The project team has developed this framework and implemented it with a multi-scale model for simulating creep of a core reactor cladding. The multi-scale model is composed of the viscoplastic self-consistent (VPSC) code at the meso-scale, which represents the visco-plastic behavior and changing properties of a highly anisotropic material and a Finite Element (FE) code at the macro-scale to represent the elastic behavior and apply the loading. The framework developed takes advantage of the transparency provided by partitioned analysis, where independent constituent codes are coupled in an iterative manner. This transparency allows model developers to better understand and remedy the source of biases and uncertainties, whether they stem from the constituents or the coupling interface by exploiting separate-effect experiments conducted within the constituent domain and integral-effect experiments conducted within the full-system domain. The project team has implemented this procedure with the multi- scale VPSC-FE model and demonstrated its ability to improve the predictive capability of the model. Within this framework, the project team has focused on optimizing resource allocation for improving numerical models through further code development and experimentation. Related to further code development, we have developed a code prioritization index (CPI) for coupled numerical models. CPI is implemented to effectively improve the predictive capability of the coupled model by increasing the sophistication of constituent codes. In relation to designing new experiments, we investigated the information gained by the addition of each new experiment used for calibration and bias correction of a simulation model. Additionally, the variability of ‘information gain’ through the design domain has been investigated in order to identify the experiment settings where maximum information gain occurs and thus guide the experimenters in the selection of the experiment settings. This idea was extended to evaluate the information gain from each experiment can be improved by intelligently selecting the experiments, leading to the development of the Batch Sequential Design (BSD) technique. Additionally, we evaluated the importance of sufficiently exploring the domain of applicability in experiment-based validation of high-consequence modeling and simulation by developing a new metric to quantify coverage. This metric has also been incorporated into the design of new experiments. Finally, we have proposed a data-aware calibration approach for the calibration of numerical models. This new method considers the complexity of a numerical model (the number of parameters to be calibrated, parameter uncertainty, and form of the model) and seeks to identify the number of experiments necessary to calibrate the model based on the level of sophistication of the physics. The final component in the project team’s work to improve model calibration and validation methods is the incorporation of robustness to non-probabilistic uncertainty in the input parameters. This is an improvement to model validation and uncertainty quantification stemming beyond the originally proposed scope of the project. We have introduced a new metric for incorporating the concept of robustness into experiment-based validation of numerical models. This project has accounted for the graduation of two Ph.D. students (Kendra Van Buren and Josh Hegenderfer) and two M.S. students (Matthew Egeberg and Parker Shields). One of the doctoral students is now working in the nuclear engineering field and the other one is a post-doctoral fellow at the Los Alamos National Laboratory. Additionally, two more Ph.D. students (Garrison Stevens and Tunc Kulaksiz) who are working towards graduation have been supported by this project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

The Effect of Fiber-Angle Fidelity on the Linear Response of Tow-steered Composite Plates

Composite laminate tailoring is traditionally performed by uniformly changing the in-plane ply orientation to obtain the desired mechanical performance. The emergence of tow-steered plies, where the fibers follow a prescribed curvilinear path, have increased the tailorability of composite laminates. However, characterizing the behavior of tow-steered laminates using finite element analysis is challenging because additional, and often numerous, orientation definitions may be required. The additional orientation definitions detrimentally increase the computational cost and hinder the use of advanced analysis techniques, such as Monte Carlo or uncertainty quantification, in the design process. To reduce computational cost without adversely affecting mechanics-based performance, the results of a parametric study that was used to investigate the effects of fiber-angle fidelity, element size, and tow-steered radius-of-curvature on various loading scenarios for tow-steered composite plates are presented. The three loading scenarios that were analyzed using finite element analysis included an axial tension load, an applied constant through-thickness-direction pressure load, and an axial compression load. Results for mechanics-based metrics of interest are presented and discussed for each loading scenario. Little sensitivity (less than one percent difference) to the effect of fiber-angle fidelity is observed in the mechanics-based metrics until the coarse-end of the considered range. Sensitivity to element size generally dominates the observed results for the mechanics-based metrics. Notable reductions in the preprocessing time are observed for increasingly coarse element size and fiber-rounding parameters. The preprocessing times decreased up to three orders of magnitude from a few thousand seconds to a few seconds without loss of accuracy in the mechanics-based metrics. Such increased computational performance is of particular interest to the structural design and analysis communities that may be conducting large counts of finite-element analyses, such as in other parametric studies, Monte-Carlo analyses, uncertainty quantification, or tow-steered optimization.

tow-steered composites↗

DOE OSTI2026

Automated ICRF heating surrogate modeling via machine learning

This work introduces automated machine learning workflows that address critical bottlenecks in surrogate model development for Ion Cyclotron Range of Frequencies (ICRF) heating applications. The automated framework includes data analysis tools that transform raw datasets into actionable insights in seconds, replacing weeks of manual exploratory effort and ensuring consistent, reproducible dataset characterization. By integrating advanced hyperparameter optimization (HPO) methods including Bayesian optimization via BoTorch and Tree-structured Parzen Estimators (TPE), the framework significantly reduces model development time from weeks to hours, decreasing computational cost and required expertise, while enabling high-accuracy surrogate models. Compared to traditional hyperparameter scanning (HPS) techniques such as methodical, randomized, and grid searches, HPO methods achieve superior convergence and predictive performance, even when compared to already well-tuned reference models. On NSTX High Harmonic Fast Wave (HHFW) heating datasets, both Random Forest Regressor (RFR) and neural network surrogates demonstrate improved accuracy, achieving R 2 values beyond 0.97 and 0.98, respectively. The results show that while HPO gains are modest for robust architectures like RFR, they become essential for more sensitive models such as neural networks, highlighting the trade-offs across optimization strategies. Through automated workflows that eliminate manual hyperparameter tuning and require minimal ML expertise, this work enables widespread adoption of high-fidelity surrogate models across the fusion community for real-time plasma control, uncertainty quantification, rapid experimental scenario development, and integrated system optimization.

Sanchez-Villar, Alvaro [Princeton Plasma Physics L↗

DOE OSTI2016

Probing off-Hugoniot states in Ta, Cu, and Al to 1000 GPa compression with magnetically driven liner implosions

We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Mesoscale to microscale wind farm flow modeling and evaluation

The increasing size of wind turbines, with rotors already spanning more than 150 m diameter and hub heights above 100 m, requires proper modeling of the atmospheric boundary layer (ABL) from the surface to the free atmosphere. Furthermore, large wind farm arrays create their own boundary layer structure with unique physics. This poses significant challenges to traditional wind engineering models that rely on surface-layer theories and engineering wind farm models to simulate the flow in and around wind farms. However, adopting an ABL approach offers the opportunity to better integrate wind farm design tools and meteorological models. The challenge is how to build the bridge between atmospheric and wind engineering model communities and how to establish a comprehensive evaluation process that identifies relevant physical phenomena for wind energy applications with modeling and experimental requirements. A framework for model verification, validation, and uncertainty quantification is established to guide this process by a systematic evaluation of the modeling system at increasing levels of complexity. In terms of atmospheric physics, ‘building the bridge’ means developing models for the so-called ‘terra incognita,’ a term used to designate the turbulent scales that transition from mesoscale to microscale. This range of scales within atmospheric research deals with the transition from parameterized to resolved turbulence and the improvement of surface boundary-layer parameterizations. The coupling of meteorological and wind engineering flow models and the definition of a formal model evaluation methodology, is a strong area of research for the next generation of wind conditions assessment and wind farm and wind turbine design tools. Some fundamental challenges are identified in order to direct future research in this area.

17 WIND ENERGY↗

DOE OSTI2014

Carbon Capture Simulation Initiative: A Case Study in Multi-Scale Modeling and New Challenges

Abstract: Advanced multi-scale modeling and simulation has the potential to dramatically reduce development time, resulting in considerable cost savings. The Carbon Capture Simulation Initiative is a partnership among national laboratories, industry and universities that is developing and deploying a suite of multi-scale modeling and simulation tools including basic data submodels, steady-state and dynamic process models, process optimization and uncertainty quantification tools, an advanced dynamic process control framework, high-resolution filtered computational-fluid-dynamic (CFD) submodels, validated high-fidelity device-scale CFD models with quantified uncertainty, and a risk analysis framework. These tools and models enable basic data submodels, including thermodynamics and kinetics, to be used within detailed process models to synthesize and optimize a process. The resulting process informs the development of process control systems and more detailed simulations of potential equipment to improve the design and reduce scale-up risk. Quantification and propagation of uncertainty across scales is an essential part of these tools and models.

42 ENGINEERING↗

DOE OSTI2015

Application of High Performance Computing for Studying Cyclic Variability in Dilute Internal Combustion Engines

Combustion instabilities in dilute internal combustion engines are manifest in cyclic variability (CV) in engine performance measures such as integrated heat release or shaft work. Understanding the factors leading to CV is important in model-based control, especially with high dilution where experimental studies have demonstrated that deterministic effects can become more prominent. Observation of enough consecutive engine cycles for significant statistical analysis is standard in experimental studies but is largely wanting in numerical simulations because of the computational time required to compute hundreds or thousands of consecutive cycles. We have proposed and begun implementation of an alternative approach to allow rapid simulation of long series of engine dynamics based on a low-dimensional mapping of ensembles of single-cycle simulations which map input parameters to output engine performance. This paper details the use Titan at the Oak Ridge Leadership Computing Facility to investigate CV in a gasoline direct-injected spark-ignited engine with a moderately high rate of dilution achieved through external exhaust gas recirculation. The CONVERGE™ CFD software was used to perform single-cycle simulations with imposed variations of operating parameters and boundary conditions selected according to a sparse grid sampling of the parameter space. Using an uncertainty quantification technique, the sampling scheme is chosen similar to a design of experiments grid but uses algorithms designed to minimize the number of samples required to achieve a desired degree of accuracy. The simulations map input parameters to output metrics of engine performance for a single cycle, and by mapping over a large parameter space, results can be interpolated from within that space. This interpolation scheme forms the basis for a low-dimensional ‘metamodel’ (or model of a model) which can be used to mimic the dynamical behavior of corresponding high-dimensional simulations. Simulations of high-EGR spark-ignition combustion cycles within a parametric sampling grid were performed and analyzed statistically, and sensitivities of the physical factors leading to high CV are presented. With these results, the prospect of producing low-dimensional metamodels to describe engine dynamics at any point in the parameter space will be discussed. Additionally, modifications to the methodology to account for nondeterministic effects in the numerical solution environment are proposed.

Finney, Charles E. A.↗

DOE OSTI2019

Thermal Transport and Fracture Behavior of Sintered Fuel Pellets: Experimental Validation of NEAMS Tool MARMOT

The project targets at experimental validation of NEAMS tool MARMOT for predicting thermal transport and fuel fracture. The key components of the project include: (1) sintering UO 2 samples with well-controlled microstructures (grain size, pore, fission bubble, porosity and pore distribution either in intra- or inter-granular pores); (2) thermal conductivity measurements of these wellcharacterized polycrystalline samples; (3) indentation testing of sintered UO 2 with various grain size, porosity and stoichiometry to obtain fracture and crack propagation mechanisms (inter or intragranular fracture); and (4) validation and uncertainty quantification of the MARMOT thermal transport and fracture models. The high quality experimental data will be used to validate the predictions of MARMOT for thermal transport and fracture, using average data and local microstructure information. In this work, UO 2 fuels with controlled microstructure (grain size, pore size/structure and fuel chemistry) were successfully prepared by high energy ball milling of the hyper-stoichiometric UO 2+x powders purchased commercially, and consolidated by spark plasma sintering. Dense nano-sized UO 2 fuel pellets with controlled stoichiometry were sintered by SPS. The effects of different SPS sintering parameters on the pore size and distribution were investigated, and the correlation among the SPS parameter – microstructure control – stoichiometry/defect structure was established. To further control the pore structure and fuel chemistry, systematic thermal annealing of the sintered fuels with the controlled pore structure was performed in a reduced. The controlled microstructure and fuel chemistry enable the investigation of the separate effects of pore structure and fuel chemistry on thermal transport behavior. The mechanical properties of the sintered UO 2 fuels were tested by nanoindentation and microindentation testing at different temperatures. The fracture behavior of the sintered fuels as functions of grain structure and temperature was investigated. Nanocrystalline UO 2 display higher hardness than microcrystalline counterpart, consistent with the Hall-Petch strengthening mechanism. Greater Young’s modulus and fracture toughness are also identified for the nanocrystalline UO 2 , and hardness and Young’s modulus decrease with temperature, suggesting better ductility of oxide fuels at greater temperature at small length scale. Hyper-stoichiometric UO 2 specimen displays higher hardness and fracture toughness than stoichiometric UO 2 , due to the impediment of the crack propagation by the oxygen interstitial atoms. These results are useful in understanding the mechanical properties of the high burn-up structure (HBS) formed in nuclear fuels during reactor operation, and also provide critical experimental data as the input for the development and validation of the MARMOT fracture model of nuclear fuels. The thermal properties of the sintered UO 2 fuel pellets with controlled grain structure, fuel chemistry and pore structures are measured by laser flash and the impact of the microstructure characteristics on the thermal transport properties is elucidated. Through a close collaboration with the MARMOT team at Idaho National Laboratory, the thermal properties of the sintered oxide fuel pellets with controlled microstructures are measured experimentally, and modeled using the developed MARMOT thermal transport models for a joint effort of demonstrating high spatial resolution measurements at the microstructural level on as-fabricated nuclear fuels and materials and obtain critical experimental data for model validation and properties predictions. In this work, we also conducted sensitivity analysis and uncertainty quantification (UQ) on a mesoscale simulation that has been applied to understand the effective thermal conductivity of UO 2 reactor fuel using the MARMOT tool. We also conduced UQ on mechanistic macroscale models that have been developed to predict the effective thermal conductivity. The most sensitive parameter is the thermal conductivity of bulk UO 2 for the thermal conductivity models. In the future, the predicted simulation distributions need to be compared to experimental data for validation of the models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Uncertainty bounds for multivariate machine learning predictions on high-strain brittle fracture

Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in crack length, location, and orientation, which is inherently found in real-world materials. Constructing a machine learning emulator can make the process faster by orders of magnitude. There has been little work, however, on assessing the error associated with their predictions. Estimating these errors is imperative for meaningful overall uncertainty quantification. In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator. Overall, we find that the response prediction is accurate within its predicted errors, but with a somewhat conservative estimate of uncertainty.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Posterior Regularized Bayesian Neural Network incorporating soft and hard knowledge constraints

Neural Networks (NNs) have been widely used in supervised learning due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. Furthermore, the experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

14 SOLAR ENERGY↗

DOE OSTI2020

Nuclear data uncertainty propagation and modeling uncertainty impact evaluation in neutronics core simulation

Uncertainty analysis is a critical requirement in reactor simulation as it is used to quantify the reliability of best-estimate calculation. A comprehensive uncertainty analysis should characterize all sources of uncertainties in a computationally-feasible and scientifically-defendable manner. Here we employ a well-established reduced order modeling (ROM) based uncertainty quantification methodology to propagate uncertainties throughout neutronic calculations. ROM relies on recent advances in randomized data mining techniques applied to large data streams. In our proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameter uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner. This straightforward approach, albeit efficient as compared to brute force forward and/or adjoint-based methods, often employs a number of assumptions that have been unquestioned in the literature of neutronic uncertainty analysis. This manuscript argues that these assumptions could introduce another source of uncertainty referred to as modeling uncertainties, whose magnitude needs to be quantified in tandem with nuclear data uncertainties. Thus, our primary goal is to explore the interactions between these two uncertainty sources in order to assess whether modeling uncertainties have an impact on parameter uncertainties. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified. The study employs a CANDU reactor model, with Serpent and NEWT as lattice physics solvers and NESTLE-C as core simulator. The modeling assumptions investigated include those related with the uncertainty propagation method employed, e.g., deterministic vs. stochastic, the few-group energy structure employed to represent the cross-sections, the resonance treatment in lattice physics calculation, the reference values for the cross-section, and the number of samples employed to render ROM compression. Results indicate that some of the modeling assumptions could have a non-negligible impact on the core responses propagated uncertainties, highlighting the need for a more comprehensive approach to combine parameter and modeling uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Round Robin Measurements of Molten Salt Properties for LiF-NaF-KF (FLiNaK) and NaCl-KCl Mixtures

The development, operation, and regulation of nuclear reactors that utilize molten salts as fuel or as heat transfer media require knowledge of the thermal properties of the salt systems and quantification of the corresponding uncertainties. Knowledge of molten salt properties is also necessary for applications in material synthesis, processing, separations, solar thermal power generation, and energy storage. A round robin was conducted with national laboratory and university participants from twenty-one laboratories in five countries to compare property measurements, to better understand uncertainties, and to identify possible best practices. Two salt mixtures, each from a common batch, were distributed to participants for evaluation: equimolar NaCl-KCl and 45.0LiF-13.7NaF-41.3KF mol % (FLiNaK). Measurements were performed to determine the major constituent composition, oxygen content, density, thermal expansivity, melting point, and thermal conductivity. Error analysis was performed on each measurement for uncertainty quantification for each type of property that was explored. Finally, the resulting discussion of the methodologies used in this work is meant to lay the groundwork for the development of standard methods and reference materials for future high-temperature property measurements on halide melts.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗