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DOE OSTI2022

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Data-scarce surrogate modeling of shock-induced pore collapse process

Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2020

MAPPER – A NOVEL CAPABILITY TO SUPPORT NUCLEAR MODEL VALIDATION AND MAPPING OF BIASES AND UNCERTAINTIES

This paper overviews the initial results of a new project at the Oak Ridge National Laboratory -- supported via an internal seed funding program -- focused on the development of a novel computational capability, called MAPPER, to support model validation. The MAPPER development aims to eliminate the need for empirical criteria, such as similarity indices, often employed to identify applicable experiments for given application conditions. To achieve that, MAPPER employs an information-theoretic-based approach, based on the Kullback-Leibler (KL) divergence principle, to combine responses of available or to-be-built experiments with application responses of interest using a training set of samples generated using randomized execution of the experiments and the application high fidelity analysis models. These samples are condensed using reduced order modeling techniques in the form of a joint probability distribution function (PDF) connecting each application response of interest with a new effective experimental response. The initial focus of the MAPPER capability will be to support the confirmatory analysis required for criticality safety analysis of storage facilities which require k-eff biases to be known for safe operation. This paper reports some of the initial results obtained with MAPPER as applied to a set of critical experiments for which existing similarity-based methods have been shown to provide inaccurate estimates of the biases.

Mertyurek, Ugur↗

DOE OSTI2020

Evaluation of Engineered Barrier Systems (FY19 Report)

This report describes research and development (R&D) activities conducted during fiscal year 2019 (FY19) specifically related to the Engineered Barrier System (EBS) R&D Work Package in the Spent Fuel and Waste Science and Technology (SFWST) Campaign supported by the United States (U.S.) Department of Eneregy (DOE). The R&D activities focus on understanding EBS component evolution and interactions within the EBS, as well as interactions between the host media and the EBS. A primary goal is to advance the development of process models that can be implemented directly within the Genreric Disposal System Analysis (GDSA) platform or that can contribute to the safety case in some manner such as building confidence, providing further insight into the processes being modeled, establishing better constraints on barrier performance, etc.The FY19 EBS activities involved not only modeling and analysis work, but experimental work as well. The report documents the FY19 progress made in seven different research areas as follows: (1) thermal analysis for the disposal of dual purpose canisters (DPCs) in sedimentary host rock using the semianalytical method, (2) tetravalent uranium solubility and speciation, (3) modeling of high temperature, thermal-hydrologic-mechanical-chemical (THMC) coupled processes, (4) integration of coupled thermalhydrologic- chemical (THC) model with GDSA using a Reduced-Order Model, (5) studying chemical controls on montmorillonite structure and swelling pressure, (6) transmission x-ray microscope for in-situ nanotomography of bentonite and shale, and (7) in-situ electrochemical testing of uranium dioxide under anoxic conditions. The R&D team consisted of subject matter experts from Sandia National Laboratories, Lawrence Berkeley National Laboratory (LBNL), Los Alamos National Laboratory (LANL), Pacific Northwest National Laboratory (PNNL), the Bureau de Recherches Géologiques et Minières (BRGM), the University of California Berkeley, and Mississippi State University. In addition, the EBS R&D work leverages international collaborations to ensure that the DOE program is active and abreast of the latest advances in nuclear waste disposal. For example, the FY19 work on modeling coupled THMC processes at high temperatures relied on the bentonite properties from the Full-scale Engineered Barrier EXperiment (FEBEX) Field Test conducted at the Grimsel Test Site in Switzerland. Overall, significant progress has been made in FY19 towards developing the modeling tools and experimental capabilities needed to investigate the performance of EBS materials and the associated interactions in the drift and the surrounding near-field environment under a variety of conditions including high temperature regimes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Delivery of Dynamic Thermal Energy Storage Models and Advanced Reactor Concept Models to the HYBRID Repository

This publication details newly created energy storage and reactor models developed within the HYBRID modeling repository as part of the Department of Energy Office of Nuclear Energy (DOE-NE) Integrated Energy Systems (IES) program, led by Idaho National Laboratory (INL). Model development to-date includes creation of dynamic systems-level models of a pebble bed high temperature gas reactor (HTGR), sodium fast reactor (SFR), compressed air energy storage (CAES), liquid air energy storage (LAES) and Modelica standard library based two-tank sensible heat storage (SHS) in the IES-based HYBRID repository. Models are developed using the latest publicly available data and incorporate the possibility of control strategy inclusion for use with the existing IES modeling, analysis, and optimization toolset. Simulations showcase the abilities of each technology to flexibly operate in ways consistent with IES operation expectations. When these models are available, they can be utilized within different integrated energy park concepts to understand optimal system operation, control, and dispatching. Moreover, given the generic nature of the models, industrial partner technologies can be quickly added to the repository using the existing models as a basis. Additional dynamic models for thermal energy storage concepts can be developed and added to the HYBRID repository as needed. Also detailed in this report are future development goals for the HYBRID repository including adding suites of steady-state models, economic costing information, and reduced-order models. By adding these models in addition to the physical transient models currently existing within HYBRID, HYBRID will be a fully integrable tool for FORCE users.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Physics-Reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery

The central objective of this project was to address the challenge of modeling and simulating complex multiscale turbulence phenomena by leveraging physics-guided machine learning (PGML) and hybrid modeling approaches. By integrating physics-based methods with data-driven models, the research focused on achieving robust and scalable solutions for geophysical turbulence, enhancing numerical weather prediction and climate research tools. The project resulted in significant advancements in computational modeling paradigms, predictive tools for reduced-order modeling, and innovative algorithms for fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Discrete Empirical Interpolation Method Based Dynamic Load Model Reduction

Dynamic load models add significant complexity to bulk power system time-domain simulations. The complexity is due to the large number of ordinary differential equations (ODEs) introduced by the dynamic load components such as induction motors. It is challenging to derive reduced-order models (ROMs) for dynamic loads due to the nonlinear functions in their governing equations. This paper applies the discrete empirical interpolation method enhanced proper orthogonal decomposition (DEIM-POD) to approximate the full dynamic load model with the ROM that minimizes the projection error of the nonlinear functions in dynamic load ODEs onto their dominant modes. This approach only requires evaluation of nonlinear functions at selected observation points. The observation points selected by DEIM also provide information for screening critical load buses where dynamic load model parameters contribute the most to the accuracy of ROM across multiple contingencies. The proposed approach is validated on IEEE 9-bus, WECC 179-bus and 2384-bus Polish systems.

bulk power system↗

DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

DOE OSTI2025

Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis

The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Deep learning model for fast, science-based forecasting of fluid migration along faults in geologic carbon storage scenarios

Effective long-term geologic storage depends on robust site selection and credible, science-based forecasting of subsurface behavior to ensure storage integrity. For this work, we develop a deep learning–based reduced-order model (ROM) to quantify potential carbon dioxide (CO₂) and brine migration through geological faults. The ROM combines a Transformer model for binary classification and a Stacked Ensemble for regression, trained on a comprehensive dataset generated from 1400 physics-based reservoir simulations. Key geologic and operational parameters—including fault geometry, reservoir structure, and injection conditions—were systematically varied to capture a wide range of fluid migration scenarios. The ROM accurately predicts the onset of migration, cumulative migration volumes of both CO₂ and brine, and associated migration rates, as compared to an independent set of validation simulations, while significantly reducing computational cost compared to traditional simulation methods. Model performance was evaluated across diverse fault configurations, revealing that shallow reservoir geometry and fault angle are among the most influential factors governing migration behavior. Sensitivity analysis using SHapley Additive exPlanations (SHAP) provided interpretability, revealing distinct patterns in how geological and operational features drive transient versus cumulative migration outcomes. The ROM’s ability to rapidly simulate fault migration scenarios enables efficient sensitivity analyses, scenario evaluations, and decision support for site selection and monitoring design. This approach enhances the safety, scalability, and long-term operational performance of geologic carbon storage (GCS) systems by providing a robust, interpretable tool for predicting subsurface fluid migration and assessing fault-related migration potential.

42 ENGINEERING↗

DOE OSTI2023

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Program Review

This program developed an advanced model-based monitoring and model-predictive control algorithms for a coal fired power plant (CFPP), and deployed these algorithms in a real-time platform to demonstrate performance benefits for transient flexibility and plant operation efficiency. More specifically, the objectives were successfully achieved through a combination of (i) developing a high-fidelity transient plant model in Apros, which was used as a high-fidelity plant simulation between $100-50\% TMCR$ where TMCR denotes the turbine maximum continuous rating, i.e., baseload, (ii) developing a very fast physics-based reduced-order model (ROM) of the plant, which ran more than $100\times$ faster than real-time, enabling its use as real-time embedded model for model-based estimation (MBE) and model predictive control (MPC) (iii) implementing a real-time MBE based on ROM using a robust unscented Kalman filter (UKF) to continuously tune the ROM to match the measurements from high-fidelity Apros plant model despite significant plant-model mismatch, and thus, obtain a Digital Twin of the plant (iv) designing and implementing a real-time MPC with dual objectives of transient plant load tracking with high ramp rates and minimizing coal consumption, i.e., improving plant efficiency in the baseload-partload operation range of $100-50\% TMCR$. Each key element above was developed and tested individually, and has been reported in corresponding Topical Reports. Finally, all the individual elements were integrated in an overall closed-loop system, that was successfully tested in desktop Simulink test harness simulations with ROM or high-fidelity model as the plant. Thereafter, the Simulink implementation was used to auto-generate C-code and deploy as real-time Docker microservice containers in Linux, and validate that they can run in real-time in the hardware-in-the loop (HIL) setup and produce the same results as in Simulink. The results of the integrated simulation tests in Simulink as well as the real-time HIL deployment are documented in this final report, showing good load tracking for load ramps at $3-4\%/min$ ramp rates, and achieving up to $5.5\%$ reduction in coal relative to baseline operation at $50\% TMCR$ load. The desktop and HIL simulations show successful performance of the overall model based estimation and control solution and achieve the key objectives of the program for flexible, efficient and reliable operation of sub-critical coal fired power plants.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2023

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Report

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2025

A predictive analytical model of electrical transport in multi-principal-element alloys

A predictive analytical model is presented for the electrical conductivity of multi-principal-element alloys (MPEAs), including those containing aluminum, transition metals, and refractory metals. Given that the lattice parameter of the Wigner-Seitz cell of an MPEA is similarly variable to a bulk metallic glass, it is postulated that electron scattering can be approximated by a series of two-level systems. Here, the resulting reduced-order model enabled an accurate determination of electrical resistivity and electron thermal conductivity based on the scattering of electrons in a two-level system across a Bloch-potential-based virtual crystal approximation. Model results are compared to experimental four-point probe electrical resistivity measurements between 300 K and 700 K for Al 0.3 CoCrCuFeNi, CoCrFeMnNi, (CoCrFeMnNi) 0.98 W 0.02 , (CoCrFeMnNi) 0.95 W 0.05 , and Nb 4 Ta 4 V 3 Ti, for model validation.

Analytical model↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

From Machine Learning to Nuclear Digital Twins

This presentation provides multiple case studies of Machine Learning, Uncertainty Quantification, Reduced Order Modeling, to achieve digital transformation and provide the components for nuclear digital twinning. The presentation is for an international virtual event titled: Consultancy Meeting on Applications of AI and Pattern Recognition Techniques for Uncertainty Quantification in Nuclear Power Modelling and Simulation held Oct 21-22, 2021.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Impacts of Different Operation Conditions and Geological Formation Characteristics on CO2 Sequestration in Citronelle Dome, Alabama

Major concerns of carbon dioxide (CO2) sequestration in subsurface formations are knowledge of the well injectivity and gas storage capacity of the formation, the CO2 pressure and saturation plume extensions during and after injection, and the risks associated with CO2 leakage and fault reactivation. Saline reservoirs are considered as one of the target formations for CO2 sequestration through structural, residual, dissolution, and mineral trapping mechanisms. The boundary condition of the saline reservoir dictates the pressure and saturation plume extension of the injected supercritical CO2 that could expand over large distances. This can lead to sources of risk, e.g., leakage and/or fault reactivation due to presence of wells, thief zones, and geological discontinuities. Therefore, there is a critical need to develop a model that describes how risk-related performance metrics (i.e., the CO2 saturation plume size, the pressure differential plume area, and the pressure differential at specific locations) vary as a function of the size of injection, time following injection, injection operations, and geologic environment. In this study, a systematic reservoir modeling studies of anthropogenic CO2 sequestration in Citronelle dome, Alabama, was performed where all relevant scenarios and conditions to address the questions of the saturation and pressure plume size in the area of review (AoR) and post-injection site care (PISC) are considered. The objective for this study was firstly to systematically simulate CO2 sequestration, i.e., saturation dynamics, and pressure behavior over a range of operational and geological conditions and to derive conclusions about the factors influencing saturation and pressure plume size, post-injection behavior, and the risk associated with them, by developing third-generation reduced order models (ROMs) for reservoir behavior. Finally, to assess the uncertainty associated with our studies, Latin Hypercube Sampling (LHS) together with an experimental design technique, i.e., Plackett–Burman design, was used. Application of Pareto charts and respond surfaces enabled us to determine the most important parameters impacting saturation and pressure plume sizes and to quantify the auto- and cross-correlation among different parameters in both history-matched and upscaled models.

58 GEOSCIENCES↗

DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗