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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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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2021

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Machine Learning Reduced Order Model for Cost and Emission Assessment of a Pyrolysis System

Biomass pyrolysis is a promising approach for producing economic and environmentally-friendly fuels and bioproducts. Biomass pyrolysis experiments show that feedstock properties have a significant impact on product yields and composition. Scientists are developing detailed chemical reaction mechanisms to capture the relationships between biomass composition and pyrolysis yields. These mechanisms can be computationally intensive. In this study, we investigate the use of a machine learning reduced order model (ROM) for assessing the costs and emissions of a pyrolysis biorefinery. Here, we developed a Kriging-based ROM to predict pyrolysis yields of 314 feedstock samples based on the results of a detailed chemical kinetic pyrolysis mechanism. The ROM is integrated into a chemical process model for calculating mass and energy yields in a commercial-scale (2000 tonne/day) biorefinery. The ROM estimated biofuel yields of 65 to 130 gallons per ton of dry biomass. This results in biofuel minimum fuel-selling prices of $2.62 to $5.43 per gallon and emissions of -13.62 to 145 kg of CO 2 per MJ. The ROM achieved an average mean square error of 1.8e-20 and a mean absolute error of 0.53%. These results suggest that ROMs can facilitate rapid feedstock screening for biorefinery systems.

09 BIOMASS FUELS↗
DOE OSTI2025

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

coupled problems↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian operator inference for data-driven reduced-order modeling

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evaluation of Reduced Order Model for HT-9 Creep and Modifications to Current HT-9 Creep Model in BISON

In order to leverage existing reduced order models (ROM) for the modeling of LANL-developed HT-9 cladding constitutive behavior, mechanistic-based models have been implemented into BISON. It is posited that the increased fidelity of the ROM will show improvement over engineering-scale models in terms of comparison against experimental measurements. INL will assist LANL in implementing an HT9 ROM in BISON. Once the HT-9 mechanistic constitutive model can be leveraged in nuclear performance simulations, the numerical results of fast reactor models will be analyzed and compared against the Fuels Irradiation & Physics Database (FIPD) and separate effects tests to attempt a validation process. INL and LANL will work together to perform any necessary improvement that is identified during the implementation and use processes. Successful completion of the milestone will enable the general use of validated mechanistic ROMs for HT-9 cladding in BISON. This report provides a brief introduction to the Los Alamos Reduced Order Model Applied to Nonlinear Constitutive Equations (LAROMANCE) code, mechanical testing used to illustrate its creep and plastic deformation predictions for HT-9 cladding, and a comparison with existing models implemented into BISON. Current models have been modified to more appropriately account for primary thermal creep and results for corresponding testing are included in this report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The Construction of Reduced Order Models for the HYBRID Repository

Reduced order models (ROMs) present an opportunity to reduce the computational burden of IES analysis using HYBRID models without significantly sacrificing data accuracy. Other applications of ROMs are digital twins, stochastic optimization studies, model exporting, and protection of proprietary information. In this paper the capability of creating ROMs of the models within the HYBRID repository will be demonstrated. Specifically, a linear regression ROM of a gas turbine and a dynamic mode decomposition with control (DMDc) ROM of a lithium-ion battery are constructed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations.

08 HYDROGEN↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗