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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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At least 19 records
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 OSTI2015

Determining Reduced Order Models for Optimal Stochastic Reduced Order Models

The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.

42 ENGINEERING↗
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 OSTI2016

A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring [PowerPoint]

Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.

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 OSTI2017

Formulation and validation of a reduced order model of 2D materials exhibiting a two-phase microstructure as applied to graphene oxide [Formulation and validation of a reduced order model of 2D materials exhibiting a two-phase microstructure]

Novel 2D materials, e.g., graphene oxide (GO), are attractive building blocks in the design of advanced materials due to their reactive chemistry, which can enhance interfacial interactions while providing good in-plane mechanical properties. Recent studies have hypothesized that the randomly distributed two-phase microstructure of GO, which arises due to its oxidized chemistry, leads to differences in nano- vs meso–scale mechanical responses. However, this effect has not been carefully studied using molecular dynamics due to computational limitations. Herein, a continuum mechanics model, formulated based on density functional based tight binding (DFTB) constitutive results for GO nano-flakes, is establish for capturing the effect of oxidation patterns on the material mechanical properties. GO is idealized as a continuum heterogeneous two-phase material, where the mechanical response of each phase, graphitic and oxidized, is informed from DFTB simulations. A finite element implementation of the model is validated via MD simulations and then used to investigate the existence of GO representative volume elements (RVE). We find that for the studied GO, an RVE behavior arises for monolayer sizes in excess to 40 nm. Moreover, we reveal that the response of monolayers with two main different functional chemistries, epoxide-rich and hydroxyl–rich, present distinct differences in mechanical behavior. In addition, we explored the role of defect density in GO, and validate the applicability of the model to larger length scales by predicting membrane deflection behavior, in close agreement with previous experimental and theoretical observations. As such the work presents a reduced order modeling framework applicable in the study of mechanical properties and deformation mechanisms in 2D multiphase materials.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables. (C) 2014 Elsevier B.V. All rights reserved.

Stetzel, KD↗