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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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Robust Design Under Uncertainty of Hypersonic Inlets

The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.

Hypersonic↗
DOE OSTI2018

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Gaussian process regression↗
DOE OSTI2023

Complete quantification of parametric uncertainties in ( d , p ) transfer reactions

Deuteron-induced transfer reactions are a popular probe in nuclear structure and nuclear astro physics studies. The interpretation of these transfer measurements relies on reaction theory that takes as input effective interactions between the nucleons and the target nucleus. Previous work quantified the uncertainty associated with the optical potentials between the nucleons and the target. In this study, we extend that work by also including the parameters of the mean field associated with the overlap function of the final bound state, thus obtaining the full parametric uncertainty on transfer observables. We use Bayesian Markov Chain Monte Carlo simulations to obtain parameter posterior distributions. We use elastic-scattering cross sections to constrain the optical potential parameters and use the asymptotic normalization coefficient of the final state to constrain the bound state interaction. We then propagate these posteriors to the transfer angular distributions and obtain confidence intervals for this observable. We study (d,p) reactions on 14 C, 16 O, and 48 Ca at energies in the range $E$ $d$ = 7 - 24 MeV. Our results show a strong reduction in uncertainty by using the asymptotic normalization coefficient as a constraint, particularly for those reactions most sensitive to ambiguities in the mean field. For those reactions, the importance of constraining the bound state interaction is equal to that of constraining the optical potentials. Furthermore, the case of 14 C is an outlier because the cross section is less sensitive to the nuclear interior. When minimal constraints are used on the parameters of the nucleon-target interaction, the 1σ uncertainties on the differential cross sections are large (~ 500-100%). However, if elastic-scattering data and the asymptotic normalization coefficient are used in the analysis, with an error of 10% (5%), this uncertainty reduces to ~ 30% (~ 15%).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Probabilistic neural networks for improved analyses with phenomenological R -matrix

Here we present a method for measurement analyses based on probabilistic deep neural networks that provide several advantages over conventional analyses with phenomenological models. These include predicting physical quantities directly from data, the rapid generation of statistically robust uncertainties, and the ability to bypass some parameters that may induce ambiguities and complications in data analysis. As deep learning methods make predictions through “black boxes,” the uncertainty quantification is typically challenging. We use a probabilistic framework that provides thorough uncertainty quantification and is straightforward to follow in practice. With the network architecture based on the Transformer, we demonstrate the current method for predicting nuclear resonance parameters from scattering data using the phenomenological R-matrix model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Learning-Based Inversion-Free Model-Data Integration to Advance Ecosystem Model Prediction

Ecosystem model prediction is important for understanding ecosystem responses to climate change and for management support. Model prediction and quantification of predictive uncertainty of ecosystems have long been investigated. The traditional workflow, which calibrates models to match observations and then uses the calibrated models for predictions, relies heavily on inverse modeling to constrain uncertain parameters in complex forward models. This inversion-based prediction approach is infeasible for complex models with heterogeneous parameter uncertainties and incapable of rapid integration of streaming and multiple sources of data because of the difficulty and computational cost in the model inversion, which is typically ill-posed and can require hundreds of thousands of expensive forward simulations to be performed iteratively. We propose to circumvent inverse modeling by precomputing an ensemble of unconstrained forward simulations and then using machine learning (ML) methods to learn the statistical relationship between simulated observation and prediction quantities. Once the ML model has learned the relationship, it can be used to make predictions of future system behavior with uncertainty quantification based on observations. The proposed learningbased inversion-free model prediction (LIMP) framework is computationally efficient which only requires a few thousands of fully parallelizable forward simulations. Additionally, LIMP can continually update predictions based on streaming observations from multiple locations and sources without necessarily requiring extra model simulations. In this study, we apply LIMP to a regional terrestrial ecosystem model with 47 parameters for testing, refining, and evaluating the approach. We demonstrate that LIMP can be used for efficient model prediction, rapid data assimilation, and cost-effective experimental design for improving robust predictive understanding of ecosystems.

Lu, Dan↗
DOE OSTI2015

Whitepaper prepared for DOE Workshop on Integrated Simulations for Magnetic Fusion Energy Sciences: Topic E: Beyond interpretive simulations

Predictive simulations of magnetic confinement fusion and burning plasmas will require the quantification of all uncertainties and errors relating to the simulation capabilities. These include: discretization error (temporal and spatial); incomplete convergence error (nonlinear, linear, etc.); uncertainties in input data (initial conditions, boundary conditions, coefficients, thermo-physical properties, source terms, etc.); and uncertainties in the component models (the specific form and parameter values).13 Typically, there is a focus on model parameter uncertainties but uncertainties about which model to use and about the bias or discrepancy of a particular model (sometimes called model form error) often dominate parameter uncertainty. This whitepaper addresses the challenges of performing uncertainty quantification (UQ) for expensive computational models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Probabilistic Geomechanical Analysis of Compartmentalization at the Snøhvit CO 2 Sequestration Project

Pressure build-up caused by large-scale CO 2 injection is one of the key concerns during a carbon sequestration project. Large overpressures can potentially compromise seal integrity, reactivate faults, and induce concerning seismicity, among other hazards. Furthermore, pressure build-up is directly related with storage capacity. In this work we study the geomechanical response to CO 2 injection in the Tubåen Fm at Snøhvit, with the objective of understanding the potential for fault reactivation, leakage, and contamination of the producing interval in an adjacent block through the bounding faults. Furthermore, we evaluate the potential contribution of a structural component to reservoir compartmentalization. We combine simplified analytical models, based on critically stressed fracture theory and a Mohr-Coulomb failure criterion, with a quantitative risk assessment methodology to perform a rigorous uncertainty quantification. Large stress uncertainties are present and are reflected in the modeling results. It was found that under the “most likely” stress state (Strike-Slip and North-South maximum horizontal stress (S Hmax ) azimuth) the faults are fairly stable, and tensile hydrofracturing of the caprock would be expected before fault reactivation. In most of the analyzed cases, the critical pressure perturbation needed for reactivation is above 13 MPa, which was the limiting pressure increase before reaching the fracture pressure. Faults were found to be ~ 20% less stable when considering plausible variations in the orientation of S Hmax . In those cases, fault reactivation could be expected before caprock failure if injection continued, posing risks of induced seismicity, CO 2 leakage and/or contamination of the gas producing reservoir. Finally, a potential structural component in the compartmentalization and fluid migration is difficult to assess due to stress orientation uncertainty.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Assessment of coated cladding impact on large-break LOCA with TRACE-DAKOTA

Since 2011, the U.S. Department of Energy has launched new research and development (R&D) programs for developing new accident tolerant fuels (ATFs). These new fuel concepts are expected to bring several advancements in terms of plant safety. However, development, licensing, as well as deployment of ATF require a substantial investment among fuel vendors, operating utilities, and regulatory authorities. For ATF to be economically feasible, credited safety benefits may be necessary to provide an economic incentive for transition of nuclear power plants from Zr/UO2-based fuel technologies to ATFs. As a result, it is essential to evaluate the economic viability of ATF by conducting a comprehensive safety benefits study informed by R&D and demonstration studies. In the present work, based on the best estimate plus uncertainty methodology, sensitivity analysis and uncertainty quantification for key safety quantities under LB-LOCA are performed for the Peach Bottom boiling water reactor (BWR) with GE14 nuclear fuel design adopting the ATF concepts. A coupled TRACE-DAKOTA analysis framework is adopted to perform the uncertainty quantification. Based on the computational results and obtained statistics, the coping time increase, fuel performance improvement as well as the most dominating phenomena during the accident for Cr-coated cladding are investigated in detail. Overall, the results obtained are useful for subsequent plant PRA study and support a move to more modernized performance-based regulatory requirements to realize plant economic benefits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Initial development of a generic fluoride salt-cooled reactor model

Fluoride high-temperature reactors (FHRs) are high-temperature, low-pressure reactor concepts that use tri-structural isotropic (TRISO) fuel and molten fluoride salt coolant. These reactors have the potential to provide both electrical power and high-temperature process heat. We used generic FHR parameters for a pebble-bed FHR to develop an initial model with fresh fuel for a generic FHR (gFHR) in MELCOR and SCALE (NEWT and KENO). In this paper, we present the development of our gFHR models, which will serve as the baseline for a sensitivity and uncertainty analysis to quantify the range of possible source terms for FHRs in severe accidents. We present MELCOR results for fuel and coolant temperatures through the core, a nodalization study for the steady-state thermal hydraulic model, and development of reactor physics models in SCALE. As this work progresses, these models will be used to calculate source terms for a loss-of-forced-flow accident and to conduct a sensitivity study on this accident to establish a range of possible source terms. SCALE will provide reactor physics parameters like isotopic inventory, decay heat generation, and temperature coefficients of reactivity. Using the uncertainty quantification tools within SCALE, we will generate distributions for those parameters and will use the uncertainty quantification code RAVEN or DAKOTA to sample those distributions in MELCOR to quantify the impact of reactor physics and thermal hydraulic uncertainties on FHR source terms. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Predicting Flow in Fracture Networks With Quantum Algorithms

Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.

58 GEOSCIENCES↗
DOE OSTI2016

User Guidelines and Best Practices for CASL VUQ Analysis Using Dakota

In general, Dakota is the Consortium for Advanced Simulation of Light Water Reactors (CASL) delivery vehicle for verification, validation, and uncertainty quantification (VUQ) algorithms. It permits ready application of the VUQ methods described above to simulation codes by CASL researchers, code developers, and application engineers. More specifically, the CASL VUQ Strategy [33] prescribes the use of Predictive Capability Maturity Model (PCMM) assessments [37]. PCMM is an expert elicitation tool designed to characterize and communicate completeness of the approaches used for computational model definition, verification, validation, and uncertainty quantification associated with an intended application. Exercising a computational model with the methods in Dakota will yield, in part, evidence for a predictive capability maturity model (PCMM) assessment. Table 1.1 summarizes some key predictive maturity related activities (see details in [33]), with examples of how Dakota fits in. This manual offers CASL partners a guide to conducting Dakota-based VUQ studies for CASL problems. It motivates various classes of Dakota methods and includes examples of their use on representative application problems. On reading, a CASL analyst should understand why and how to apply Dakota to a simulation problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

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 continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Machine learning enhanced predictions of ICRF heating: Overcoming numerical limitations via data curation

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λ i ≫ 1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R 2 ∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Artificial neural networks↗
DOE OSTI2016

Estimation of Uncertainties of Wall Temperature Accomplished by Model Calibration Technique Using Small to Large Scale Reflooding Test Data

The fidelity of the prediction can be evaluated by performing validation and uncertainty quantification with suitable test data. Nuclear power plant design and operation must accommodate the uncertainties in predicting system performance, where those uncertainties originating due to initial and boundary conditions, numerics, and modeling uncertainties. To improve the prediction of the reactor system performance, these various sources of uncertainties can be refined through model calibration technique. The objective of this work is to refine the model parameters and to estimate the uncertainties on parameters/responses during reflood phase. To accomplish this experiments should be performed, data collected, and the data utilized to complete model calibration for the thermal-hydraulic input parameters. Simulations were performed using Safety and Performance Analysis Code (SPACE) developed by multiple research institutes in South Korea to predict the thermal hydraulic system behaviors of nuclear power plants. Since existing experimental data were obtained from several tests performed at the small scale, scaling considerations must be addressed during the uncertainty quantification process. (authors)

42 ENGINEERING↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗
DOE OSTI2020

Effects of Photovoltaic Module Materials and Design on Module Deformation Under Load

Quasi-static structural finite-element models of an aluminum-framed crystalline silicon photovoltaic module and a glass-glass thin-film module were constructed and validated against experimental measurements of deflection under uniform pressure loading. Specific practices in the computational representation of module assembly were identified as influential to matching experimental deflection observations. Additionally, parametric analyses using Latin hypercube sampling were performed to propagate input uncertainties related to module materials, dimensions, and tolerances into uncertainties in simulated deflection. Sensitivity analyses were performed on the uncertainty quantification datasets using linear correlation coefficients and variance-based sensitivity indices to elucidate key parameters influencing module deformation. Results identified edge tape and adhesive material properties as being strongly correlated to module deflection, suggesting that optimization of these materials could yield module stiffness gains at par with the conventionally structural parameters, such as glass thickness. This exercise verifies the applicability of finite-element models for accurately predicting mechanical behavior of solar modules and demonstrates a workflow for model-based parametric uncertainty quantification and sensitivity analysis. Finally, applications of this capability include the assessment of field environment loads, derivation of representative loading conditions for reduced-scale testing, and module design optimization, among others.

42 ENGINEERING↗
DOE OSTI2022

Estimation of process steady state with autoregressive models and Bayesian inference

To improve efficiency, separations engineers will typically design process circuits containing recirculating streams, which mix one or more of the process outputs with the feed material. Doing so can improve efficiency, but will cause a delay in the system reaching steady state conditions until the recirculating load mass flows stabilize. In testing separation circuits, engineers will often test a variety of factors and complete an analysis from sample results. Knowledge of if a process is at steady state, as well as the steady state conditions of a process, is essential for a valid techno-economic analysis. However, the definition of process steady state is often poorly defined, or does not include uncertainty quantification. If the performance of a process operating under two different sets of conditions are compared, an engineer who does not test for steady state or quantify steady state conditions risks producing a faulty analysis. In this work, a Bayesian statistical method for testing if all streams are at steady state is further motivated and then derived. Then after testing for steady state, the same model is used with a prior distribution that enforces a steady state assumption to estimate steady state conditions. Further, these methods were validated in a solvent extraction pilot plant where steady state conditions for all outflows were inferred with uncertainty quantification. Analysis is completed with functions available to the reader as part of the BayesMassBal (V 1.1.0) software package written in R.

01 COAL, LIGNITE, AND PEAT↗