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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Global System Reduction Order Modeling for Localized Feature Inclusion

The development of reduced-order models remains an active research area, despite advances in computational resources. Here we develop a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

42 ENGINEERING↗
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Hybrid Energy System Workflow for Energy Portfolio Optimization

This manuscript develops a workflow, driven by data analytics algorithms, to support the optimization of the economic performance of an Integrated Energy System. The goal is to determine the optimum mix of capacities from a set of different energy producers (e.g., nuclear, gas, wind and solar). A stochastic-based optimizer is employed, based on Gaussian Process Modeling, which requires numerous samples for its training. Each sample represents a time series describing the demand, load, or other operational and economic profiles for various types of energy producers. These samples are synthetically generated using a reduced order modeling algorithm that reads a limited set of historical data, such as demand and load data from past years. Numerous data analysis methods are employed to construct the reduced order models, including, for example, the Auto Regressive Moving Average, Fourier series decomposition, and the peak detection algorithm. All these algorithms are designed to detrend the data and extract features that can be employed to generate synthetic time histories that preserve the statistical properties of the original limited historical data. The optimization cost function is based on an economic model that assesses the effective cost of energy based on two figures of merit: the specific cash flow stream for each energy producer and the total Net Present Value. An initial guess for the optimal capacities is obtained using the screening curve method. The results of the Gaussian Process model-based optimization are assessed using an exhaustive Monte Carlo search, with the results indicating reasonable optimization results. The workflow has been implemented inside the Idaho National Laboratory’s Risk Analysis and Virtual Environment (RAVEN) framework. The main contribution of this study addresses several challenges in the current optimization methods of the energy portfolios in IES: First, the feasibility of generating the synthetic time series of the periodic peak data; Second, the computational burden of the conventional stochastic optimization of the energy portfolio, associated with the need for repeated executions of system models; Third, the inadequacies of previous studies in terms of the comparisons of the impact of the economic parameters. The proposed workflow can provide a scientifically defendable strategy to support decision-making in the electricity market and to help energy distributors develop a better understanding of the performance of integrated energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Reduced Models for Chemical Kinetics derived from Parallel Ensemble Simulations of Stirred Reactors

Detailed chemical kinetic models are essential to improve the predictive capability of computational fluid dynamics (CFD) simulations and to impact the development of next generation combustion technologies. However, such detailed kinetic models are beyond the reach of CFD codes due to the computational cost of transporting additional chemical degrees of freedom. Reduced order models for combustion kinetics exploit the presence of lower dimensional manifolds in the state space and require far fewer number of scalars to be transported as part of CFD simulations. In this paper, we describe the software infrastructure developed to allow large ensembles of stirred reactor configurations with detailed chemical kinetics. The canonical reactor simulations are incorporated in a workflow with sparse grid and data reduction methodologies aimed at development of reduced order models. We present results from analyzing the results of the stirred reactor calculations for syngas mixture using principal component analysis (PCA) and neural network methodologies. The results show that nonlinear autoencoder model can surpass PCA in representing the original dataset with far fewer degrees of freedom.

Zhang, Pei↗
DOE OSTI2022

Operator inference for non-intrusive model reduction with quadratic manifolds

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.

42 ENGINEERING↗
DOE OSTI2022

Data-driven wind turbine wake modeling via probabilistic machine learning

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions and the interaction between wakes. Physics-based models that capture the wake flow field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced-order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

Deep neural networks↗
DOE OSTI2024

Optimization-Based Model Reduction Scheme for Renewable Energy Power Plants Using Standardized Testing Scenarios

This paper presents an optimization-based model reduction scheme for renewable energy (RE) power plants consisting of inverter-based resources (IBRs) operating in grid-following (GFL) or grid-forming (GFM) modes. More importantly, the datasets feeding the optimization-based model reduction scheme are generated and re-used through the standardized grid-interactive testing scenarios. Particularly, the proposed scheme makes use of the power plant point of common coupling (PCC) measurements of various quantities specified by standardized tests (e.g., voltage and frequency ride through) as per IEEE 2800, to estimate the parameters of the reduced-order model such that its dynamic performance aligns with the original detailed power plant model. The proposed model reduction approach does not require the parameters of individual IBRs and using standardized test data as input to the formulated optimization problem simplifies the reduced-order modelling scheme. Extensive case studies following standardized test scenarios verified the remarkable accuracy of the proposed approach.

Yallamilli, Ram S. [Purdue University]↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

U-net architected deep material network training with microstructure local field information

The Deep Material Network (DMN) has recently emerged as a powerful reduced-order modeling framework for simulating the mechanical response of heterogeneous materials such as composites. Unlike most data-driven approaches that directly learn a material’s response under prescribed loading, the DMN acts as a homogenization operator, learning the kinematic constraints and mechanical interactions of the underlying microstructure. However, traditional DMN training relies exclusively on homogenized effective properties derived from Direct Numerical Simulations (DNS), discarding the rich local field data that govern microstructural interactions. In this work, we extend the DMN framework to incorporate such local field information into the offline training process. Utilizing a U-Net architecture, we augment the DMN training objective to include the first and second statistical moments of the local stress fields obtained from linear DNS. This ensures that the learned network topology not only fits the effective stiffness but also accurately reflects the internal local stress and strain partitioning of the microstructure. The results confirm that supervising the localization process during training yields a superior surrogate model, reducing local prediction errors by an order of magnitude and significantly improving generalization to unseen nonlinear constitutive behaviors compared to traditional DMNs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Flow and heat transfer in the wake of a triangular arrangement of spheres

This research work seeks to investigate the influence of spacing and heat transfer on the wake behavior of a triangular arrangement of spheres. Four experimental configurations have been investigated at three Reynolds numbers, Re 1 = 350, Re 2 = 700, and Re 3 = 1050. Two isothermal cases were investigated with spacing between the spheres of zero and one sphere diameter, and two cases were investigated with an applied heat flux at the same spacing conditions. The time resolved particle image velocimetry results revealed various flow phenomena including flow separations, von Karman vortex shedding, and Kelvin–Helmholtz instabilities. The turbulent statistics reveal the effect of proximity and heat transfer on the time averaged values of the wake size, turbulent strengths, and Reynolds shear stress in the wake of each sphere, namely, the laminarization effects from the addition of heat and the suppression of the lead sphere wake from the proximity of the trailing spheres. These results are complemented by the application of proper orthogonal decomposition (POD) to the flow fields, which extracts the coherent structures from the flow. Here the modes that describe the coherent structures are extracted and described in detail, which provide further insight into effects of the experimental conditions on the temporal behavior of the flow. Many of the low order modes are found to be associated in pairs, corresponding to asymmetric structures or advection of a given structure downstream. The capability of POD to produce reduced order models of the flow is then utilized to facilitate vortex identification analysis. A turbulent kinetic energy based mode truncation criteria, which has been found to enhance vortex identification capability, is applied to select the POD modes and temporal coefficients to be used in the reduced order modeling. The reconstructed velocity fields are then analyzed with vortex identification algorithms to extract the vortex cores and boundaries. The combination of these approaches allows the study of the effect of proximity and heat transfer on the vortex characteristics, such as size, strength, and distribution.

42 ENGINEERING↗
DOE OSTI2021

Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multi-objective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solvent-diffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

25 ENERGY STORAGE↗
DOE OSTI2022

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

HTGR PBR Reactor Optimization Methodology

This presentation showcases the work done under the ART work package in FY23 regarding optimization and sensitivity analysis of pebble-bed reactors. The slides include a description of the problem, the proposed methodology, the developed model used for analysis, and the methodologies for sensitivity and reduced-order modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A reduced order sulfuric acid decomposition model for a nuclear-powered hybrid sulfur cycle

A reduced order model of sulfuric acid decomposition within a bayonet chemical reactor was developed to support the U. S. Department of Energy Integrated Energy System program, and address the lack of knowledge in scaling and integration for joint chemical and nuclear processes. Sulfuric acid decomposition within a bayonet reactor was modeled to provide chemical and thermodynamic data relevant to advanced nuclear reactor-driven integrated energy systems based on desired operational scale and operational conditions. The temperature range required for high-temperature advanced nuclear reactor integrated energy systems, 750-850 °C, was shown to produce reasonable agreement (within a few percent relative error) with past models and experimental data, and yielded good efficiency results for bayonet reactor operations. The results of the reduced order model agreed with previous work from Savannah River National Labs within a maximum of 3.4% error on the decomposition of sulfur trioxide, and on previous Hybrid Sulfur flowsheets from Gorensek and Summers that showed operational temperature, pressure, and composition ranges for efficiency which made the Hybrid Sulfur cycle competitive with water electrolysis. Here, the agreement with previous high-fidelity models provided a framework for future Integrated Energy System grid evaluations with an advanced nuclear reactor and large-scale hydrogen production using a mathematical model to represent chemical operations.

08 HYDROGEN↗
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↗
DOE OSTI2025

On the Efficacy of Repeat Voltage Holds for Conditioning and Calendar Life Testing of Graphite and Silicon Cells

Voltage-hold (V-hold) protocols have shown promise toward calendar lifetime analysis of cells with graphite (Gr) and silicon (Si) anodes. In this work, repeat V-holds are performed on Gr and Si cells paired with lithium iron phosphate cathodes to delineate their beneficial role in formation and conditioning. We find that V-hold at the top of charge supplements constant current cycling in conditioning the cell to higher capacities for both Gr and Si cells after the first V-hold. A reduced order model provides the irreversible capacity proportions of each V-hold. With each repeat V-hold, parasitic loss of lithium to the solid electrolyte interphase (SEI) decreases on both Gr and Si cells. Gr cells show the square-root-of-time capacity loss behavior within 200 h of V-hold, indicative of its fast relaxation and low impact of reference performance test cycles on the SEI growth. Lifetime estimates from repeat V-holds on Gr can reach years. Si exhibits longer transition times from kinetic to diffusion-limited SEI growth, evidenced by the 400 h and 200 h holds showing square-root-of-time and linear behavior, respectively. Lifetime predictions from repeat V-holds on Si only reach 1–2 months, highlighting its limitations. Recommended duration of V-holds for Si cells should be ≥400 h.

25 ENERGY STORAGE↗