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All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Achieving High Efficiency in Reduced Order Modeling for Large Scale Polycrystal Plasticity Simulations

Reduced order models for the nonlinear response of heterogeneous microstructures typically require a construction (or training) stage to build the reduced order basis. In this manuscript, an efficient model construction strategy for the eigenstrain homogenization method (EHM) is presented. The proposed strategy relies on a parallel, element-by-element, conjugate gradient solver. Near linear scaling has been achieved with respect to the number of degrees of freedom used to resolve the microstructure. Linear scaling with respect to the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. Furthermore, a parallel implementation for fast evaluation of the constructed ROM has been developed using shared memory parallelization. It has been shown that for large microstructures with ≈ 10,000 grains, the total computational cost of evaluating the nonlinear response of a polycrystal could be reduced by approximately an order of magnitude using 32 cores with respect to serial ROM simulation. The present methodology has been verified using an additively manufactured polycrystalline microstructure of a nickel-based superalloy, Inconel 625. The capability of the developed framework to construct a ROM for such large microstructures, as well as the ability of the ROM to predict average and local quantities of interest has been demonstrated.

microscale↗
NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model↗
NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model↗
NASA NTRS2012

Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

Yao, Weigang↗
NASA NTRSDate not supplied

A Data-Driven Reduced Order Model of an Isolated Rotor

There are numerous conceptual design stage rotorcraft analysis tasks which demand a high-fidelity and low cost method for rotor load distribution predictions. Considering Urban Air Mobility (UAM) vehicles aim to operate in close proximity to buildings and with unique rotor configurations, there is a significant challenge in quickly and accurately modeling rotors operating in complex, turbulent flow fields. One potential path for deriving a high-fidelity, low cost rotor model is with data-driven surrogate modeling. In this study, an initial investigation is taken to apply a proper orthogonal decomposition (POD) based reduced order model (ROM) for the purpose of pressure distribution prediction. In this study, a POD ROM was derived to produce distributed pressure predictions on rotor blades subjected to topology change due to variation in twist and taper ratio. Rotor twist was varied between 0◦, 10◦, 20◦, and 30◦ while taper ratio was varied between 1.0, 0.9, 0.8, and 0.7. All rotors consisted of a single blade. The POD ROM was validated for three demonstration cases; a high thrust rotor in hover, a low thrust rotor in hover, and a rotor in forward flight with a flight speed of M = 0.1. Results showed highly accurate distributed load predictions could be achieved at minimal computational cost. Computational cost for hovering blade surface pressure modeling was reduced from 12 hours on 440 cores to 10−5 seconds on a single core. For blade in forward flight cost was reduced from 20 hours on 440 cores to 0.6 seconds on a single core. For cases of high thrust and low thrust rotors, POD ROM was used to undergo a design optimization of the rotor such that figure of merit was maximized. Total optimization time for each case was 1 minute.

Data-Driven↗
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↗
DOE OSTI2026

Evaluation of a Reduced-Order Model for IBR Fault Response Representation via OEM Blackbox Models: Preprint

Driven by the need to capture the electromagnetic transients of transmission lines, inverter switching behavior, and detailed control systems, electromagnetic transient (EMT) studies have become increasingly important in industry, such as IBR interconnection study and fault study. However, original equipment manufacturer (OEM) inverter models typically include extensive parameters and proprietary settings that are unavailable to protection engineers. This paper introduces a data-driven, reduced-order model (ROM) developed as a PSCAD library component for use in EMT-based fault studies. The ROM replicates key OEM model behaviors without requiring detailed knowledge of control design or parameterization. The accompanying Python automation scripts streamline data generation, parameter fitting, and validation. The ROM's performance is demonstrated through comparison with both IEEE 2800-compliant and non-compliant OEM models in a real-world power system. Relay responses show nearly identical results, while simulation runtime is reduced by an average of 32.8\%, highlighting the ROM's practicality for protection engineers.

14 SOLAR ENERGY↗
DOE OSTI2024

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗
DOE OSTI2025

Reduced-order modeling for efficient cross section library development in high-temperature gas reactor pebble-bed depletion analysis

Accurate modeling of running-in and equilibrium conditions in pebble-bed reactors (PBRs) requires precise microscopic multigroup neutron cross sections. In Griffin, deterministic neutronics calculations rely on multivariate interpolation over large cross section libraries, resulting in significant memory usage and performance bottlenecks. This work, together with a companion paper on Griffin integration, explores reduced-order models (ROMs) to replace interpolation with lightweight surrogates. Several ROM techniques are benchmarked, with deep neural networks (DNNs) demonstrating superior memory efficiency, scalability, and predictive accuracy. A total of 295 DNNs were trained to build a comprehensive isotope library, integrated into Griffin through a custom LibTorch interface for depletion analysis. Initial results demonstrate that DNN-based ROMs drastically reduce memory demands while preserving accuracy, enabling finer tabulations and additional state variables without overhead. In conclusion, the framework also supports online cross section generation and real-time DNN updates through transfer learning, improving fidelity by capturing self-shielding and evolving nuclide compositions during burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗
DOE OSTI2026

A PSCAD Library Component Featuring a Reduced-Order IBR Model for EMT-Based Fault Studies

This paper presents a fully implemented inverter reduce-order-model (ROM) in an EMT simulation (PSCAD) library component for direct user utilization in protection studies. The developed inverter ROM has the following features: Equivalent to a full IBR inverter model with positive- and negative-sequence current formulation and representation A python script is developed to fully automate this process, including training data generation, ROM parameter training, updating parameters, and model verification and validation. With this PSCAD ROM library component, protection engineers can utilize a trustworthy, accurate ROM for protection studies in an easy-to-use and streamlined manner.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Evaluation of a Reduced-Order Model for IBR Fault Response Representation via OEM Blackbox Models

This paper presents a fully implemented inverter reduced-order-model (ROM) in an EMT simulation (PSCAD) library component for direct user utilization in protection studies. The developed inverter ROM has the following features: Equivalent to a full inverter-based resource (IBR) inverter model with positive- and negative-sequence current formulation and representation. A Python script is developed to fully automate this process, including training data generation, ROM parameter training, updating parameters, and model verification and validation. The ROM is validated using both IEEE 2800-compliant and non-compliant OEM modes in a real-world system, building confidence of its usability by protection engineers.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations

Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.

Radiation↗
DOE OSTI2024

Generating An Advanced Cross-section Library For HTGR Pebble Bed Depletion Calculations Using Reduced-Order Model Generation Techniques

For code development, Advanced Reactor Technologies - Gas Cooled Reactors Program (ART-GCR) rely on a collaboration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, but the cross sections generation and the methodology definition is part of this program area goals. Based on previous studies in FY23, the size of microscopic cross section libraries increases rapidly with the number of tabulations, requiring significant amount of memory and drastically slowing down the Griffin calculations when evaluating cross sections via the multivariate linear interpolation approach. Rising to these challenges, this work investigates constructing Reduced-order Models (ROMs) for the multi-group microscopic cross sections to accelerate the cross section evaluation in Griffin. A database of multigroup cross sections is first collected considering all possible parameters that a designer could change for optimization. Down-selection of the ROM techniques afterward shows Deep Neural Network (DNN) as the best candidate when jointly consider memory efficiency, predictive accuracy, computational cost, scalability, flexibility and ease of implementation of the algorithms in comparison to the multidimensional interpolation. This work develops a specific interface that enables the cross section predictions using pre-trained DNN models into Griffin leveraging the existing ROM capabilities. DNNs have been trained for all isotopes for use in Griffin. Preliminary Griffin testing shows that DNNs exhibit exceptional predictive accuracy and the use of DNNs provides orders of magnitude improvement in memory efficiency compared to conventional interpolation techniques. With such ROM techniques, it holds great promise to further increase the fidelity of the Pebble Bed Reactor (PBR) simulation by increasing the number of tabulations/state variables during cross section evaluation, while maintaining the computational cost affordable in Griffin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

A Parametric Reduced-Order Model for Inverter Short-Circuit Response in Protection Studies

This paper presents a reduced-order model (ROM) for grid-following (GFL) inverters that reproduces inverter fault current trajectories, including sub transients, transient, and steady-state phases, across a range of fault types, locations, and pre-fault operating points. . The proposed model is developed by: Constructing the positive- and negative-sequence current with parameterization fitted by large data training and fitting Validating using EMT simulation against EMT full model and demonstrating the ROM's capability to capture fault current magnitude, phase angle, and oscillatory transients. Building a standard EMT simulation platform library component for easy configuration and application.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs

A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.

Aeroservoelasticity↗