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Results for “Reduced order representation”

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 OSTI2021

Machine learning based rate optimization under geologic uncertainty

We propose a novel approach for rate optimization during a waterflood under geologic uncertainty in reservoir properties such as permeability and porosity. The traditional approach typically involves several runs of the forward simulator. This may not scale well when the optimization is to be performed at the full field-level and over multiple geologic realizations. A machine-learning (ML) based approach which is quick and scalable for rate optimization over multiple geologic realizations is proposed instead. The training data for the model is generated by running the forward simulator with randomly assigned well rates using multiple geologic realizations. A reduced order representation of the permeability heterogeneity in each of the realizations is derived using a grid connectivity transformation (GCT). This step involves finding basis functions corresponding to the different modal frequencies of the grid connectivity represented by the grid Laplacian. The projection of the heterogeneous property field along these basis functions gives the basis coefficients that form the reduced order representation. Subsequently, for each training datapoint, streamlines are traced and the minimum time of flight (TOF) representing the tracer breakthrough time at each producer is recorded. The basis coefficients and well rates are fed to a machine learning model as input and the minimum TOF at the producers forms the output of the model. This trained model can then be used along with an optimizer for computing the optimal injection rates to maximize the injection sweep efficiency. This corresponds to minimizing the variance in the minimum TOF within each well group. Different architectures of neural network are tested using 5-fold cross validation to decide the best ML model to compute the streamline time of flight. The trained model is used to perform well rate optimization over multiple realizations of geology by using a risk tolerance penalty. The optimal well rates thus obtained are compared with two cases: a) equal well rates assigned to all injectors and producers and b) well rates obtained by optimizing over a single realization without considering the uncertainty in geology. The optimal well rates are seen to offer better oil recovery and sweep efficiency than both cases.

02 PETROLEUM↗
DOE OSTI2022

Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow

We report, in fluid physics, data-driven models to enhance or accelerate time to solution are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In the context of reduced order models of high-dimensional time-dependent fluid systems, machine learning methods grant the benefit of automated learning from data, but the burden of a model lies on its reduced-order representation of both the fluid state and physical dynamics. In this work, we build a physics-constrained, data-driven reduced order model for Navier–Stokes equations to approximate spatiotemporal fluid dynamics in the canonical case of isotropic turbulence in a triply periodic box. The model design choices mimic numerical and physical constraints by, for example, implicitly enforcing the incompressibility constraint and utilizing continuous neural ordinary differential equations for tracking the evolution of the governing differential equation. We demonstrate this technique on a three-dimensional, moderate Reynolds number turbulent fluid flow. In assessing the statistical quality and characteristics of the machine-learned model through rigorous diagnostic tests, we find that our model is capable of reconstructing the dynamics of the flow over large integral timescales, favoring accuracy at the larger length scales. More significantly, comprehensive diagnostics suggest that physically interpretable model parameters, corresponding to the representations of the fluid state and dynamics, have attributable and quantifiable impact on the quality of the model predictions and computational complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗
DOE OSTI2026

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Time-dependent-bases with local CUR decomposition method for accelerating turbulent combustion simulations

Here, this study presents a novel reduced-order modeling framework, Time-Dependent Bases with Local CUR decomposition (TDB-L-CUR), designed to efficiently and accurately approximate the species transport equations in reacting flow simulations. The method extends the existing TDB-CUR approach for chemically reacting flows (Jung et al. Comput. Methods Appl. Mech. Engrg. 437 (2025) 117758), which leverages matrix decomposition techniques to form a global-in-space, time-dependent low-dimensional manifold. While TDB-CUR performs well in homogeneous systems, it may be less well-suited to spatially heterogeneous systems such as turbulent flames, where higher-rank approximations are typically required. The proposed TDB-L-CUR framework introduces two methodological extensions to the baseline approach. First, it applies unsupervised clustering to partition the physical domain into distinct regions, enabling spatially localized manifold construction, thereby reducing the rank required for the reduced-order representation. Second, it incorporates a computational singular perturbation (CSP)-based scheme for identifying and penalizing fast species, allowing for spatio-temporally adaptive mitigation of chemical stiffness. The proposed framework is validated on a hierarchy of test cases, including a one-dimensional premixed flame, a two-dimensional nonpremixed ignition case with vortex interaction, and a three-dimensional turbulent premixed flame. TDB-L-CUR significantly improves accuracy over TDB-CUR while further reducing computational cost. The fully on-the-fly formulation of TDB-L-CUR (i.e., requiring no offline training or prior knowledge) makes it a robust and scalable tool for reduced-order modeling of reactive flows.

Local manifold↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Towards Reconstruction of Complex Flow Fields Using Unit Flows

Many complex turbulent flows in nature and engineering can be qualitatively regarded as being constituted of multiple simpler unit flows. The objective of this work is to characterize the coherent structures in such complex flows as a combination of constituent unitary flow structures for the purpose of reduced-order representation. While turbulence is clearly a non-linear phenomenon, we aim to establish the degree to which the optimally weighted superposition of unitary flow structures can represent the complex flow structures. The rationale for investigating such superposition stems from the fact that the large-scale coherent structures are generated by underlying flow instabilities that may be reasonably described using linear analysis. Clearly, the degree of validity of superposition will depend on the flow under consideration. In this work, we take the first step toward establishing a procedure for investigating superposition. Experimental data of single and triple tandem jets in crossflow are used to demonstrate the procedure. A composite triple tandem jet flow field is generated from optimal superposition of single jet data and compared against ‘true’ triple jet data. Direct comparisons between the true and composite fields are made for spatial, temporal, and kinetic energy content. The large-scale features (obtained from proper orthogonal decomposition or POD) of true and composite tandem jet wakes exhibit nearly 70% agreement in terms of modal eigenvector correlation. Corresponding eigenvalues reveal that the kinetic energy of the flow is also emulated with only a slight overprediction. Temporal frequency features are also examined in an effort to completely characterize POD modes. The proposed method serves as a foundation for more rigorous and robust dimensional reduction in complex flows based on unit flow modes.

Kristo, Paul J.↗
NASA NTRS1991

Structural representation for analysis of a controlled structure

The purpose was to determine what reduced order structural representation is most appropriate for coupling with a control system. The goal was to choose a reduced order structural model which retains as closely as possible the characteristics of the closed loop model with a full order structural representation. By characteristics of the closed loop model, it is meant that the closed loop eigenvalues and the closed loop transfer functions from commands to loads and from commands to response. This process does not address the accuracy of the full order model (usually a finite element model) but only the loss of accuracy associated with reducing th model. For the purposes of this study, only collocated sensors and actuators are examined. The choice of a structural representation for noncollocated sensors and actuators is not so clear.

Blelloch, Paul A.↗
NASA NTRS1989

Numerical simulation of controlled large space structures

Large Space Structures do not have much damping, which necessitates the installation of a controller onto the structure. If the controller is improperly designed, the structure may become unstable and be destroyed. Since Large Space Structures are extremely expensive pieces of hardware, new controllers must not be tested first on the structure. They must first be tested in computer simulations. Until now, the usual procedure for simulating controlled Large Space Structures is to compute a reduced order modal representation of the structure and then apply the controller. However, this procedure entails modal truncation error. A new software package which is free from this error is currently under development within the Center for Space Construction. The more accurate finite element representation of the structure is used in the simulation, instead of the less accurate reduced order modal representation. This software also features an efficient matrix storage scheme, which effectively deals with the asymmetric system matrices which occur when control is added to the structure. Also, an integration algorithm was chosen so that the simulation is a reliable indicator of system stability or instability. The software package is fairly general in nature. Linearity of the finite element model and of the controller is the only assumption made. Actuator dynamics, sensor dynamics, noise, and disturbances can be handled by the package. In addition, output feedback of displacement, velocity, and/or acceleration signals can be simulated. Kalman state estimation was also implemented. This software was tested on a finite element model of a real Large Space Structure: The Mini-Mast Truss. Mini-Mast is a testbed at NASA-Langley which is currently under development. A 714 degree of freedom finite element model was computed, and a 19 state controller was designed for it. Torque wheel dynamics were added to the model, and the entire closed loop system was simulated with the software package.

Quan, Ralph↗
DOE OSTI2024

Reduced‐Order Modeling for Linearized Representations of Microphysical Process Rates

Abstract Representing cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical variables used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data‐driven reduced‐order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions. Using simulations characteristic of marine stratiform clouds, we simultaneously learn lower dimensional representations of droplet size distributions and predict the evolution of the microphysical state of the system. Droplet collision‐coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of three. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision‐coalescence in models. We demonstrate how deep learning based reduced‐order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision‐coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment‐based representations.

54 ENVIRONMENTAL SCIENCES↗
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↗
DOE OSTI2025

mphys-surrogate-model

This repository contains python scripts for building and studying reduced-order-modeling representations of droplet coalescence for eventual use in atmospheric models. The included data are generated from high-fidelity superdroplet methods and are utilized by machine learning pipelines to build data-driven models of droplet size distributions that evolve under coalescence. This repository further includes scripts to determine prediction (uncertainty) intervals on the data-driven model products based on conformal prediction.

Katona, JonasE [Lawrence Livermore National Labora↗
DOE OSTI2024

Adaptive Methods for Radial Basis Functions

Radial basis functions (RBFs) are a powerful tool for constructing high-order accurate reduced representations of scattered data in arbitrary dimension and on manifolds. We present a method of constructing data approximations in which we utilize a functional tail to capture a global background profile and a RBF neural network (NN) to capture the smaller-scale features. In the RBF NN the RBF centers, matrix shape parameters were selected adaptively for each RBF. We also utilized a geodesic notion of distance on the manifold on which the data lies, e.g., the spherical geodesic for data on the sphere. Although each of these ideas have been been investigated separately in previous works, their combination into a single algorithm is novel. We defined a machine learning problem in which these properties are learned to minimize the data reduction error. We demonstrate the algorithm for applications of scattered data reduction in the plane and on the sphere.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2022

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗