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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 OSTI2020

Model reduction for hypersonic aerodynamics via conservative LSPG projection and hyper-reduction

High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models. However, it is very computationally expensive to run CFD for hypersonic flows due to the fine grid resolution required to capture the strong shocks and large gradients that are typically present. Furthermore, UQ approaches are “many-query” problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model. In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems including subsonic CFD applications. This allows computationally inexpensive LSPG ROM simulations to replace the full-order model simulations in UQ studies, which makes this many-query task tractable, even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application. In particular, we present results for LSPG ROMs of the HIFiRE-1 in a three-dimensional, turbulent Mach 7.1 flow, showcasing the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.

Fluid Dynamics↗
DOE OSTI2026

Toward real-time optimization through model reduction and model discrepancy sensitivities

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs—those that do not require access to the full-order model at evaluation time—is popular because they facilitate the computation of optimization solutions within the wall-clock time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, a limited number of full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. In conclusion, the HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data.

PDE-constrained optimization↗
DOE OSTI2021

Discrete Empirical Interpolation Method Based Dynamic Load Model Reduction

Dynamic load models add significant complexity to bulk power system time-domain simulations. The complexity is due to the large number of ordinary differential equations (ODEs) introduced by the dynamic load components such as induction motors. It is challenging to derive reduced-order models (ROMs) for dynamic loads due to the nonlinear functions in their governing equations. This paper applies the discrete empirical interpolation method enhanced proper orthogonal decomposition (DEIM-POD) to approximate the full dynamic load model with the ROM that minimizes the projection error of the nonlinear functions in dynamic load ODEs onto their dominant modes. This approach only requires evaluation of nonlinear functions at selected observation points. The observation points selected by DEIM also provide information for screening critical load buses where dynamic load model parameters contribute the most to the accuracy of ROM across multiple contingencies. The proposed approach is validated on IEEE 9-bus, WECC 179-bus and 2384-bus Polish systems.

bulk power system↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Model reduction for a power grid model

We examine the complexity of constructing reduced order models for subsets of the variables needed to represent the state of the power grid. In particular, we apply model reduction techniques to the DeMarco-Zheng power grid model. We show that due to the oscillating nature of the solutions and the absence of timescale separation between resolved and unresolved variables, the construction of accurate reduced models becomes highly non-trivial because one has to account for long memory effects. In addition, we show that a reduced model that includes even a short memory is drastically better than a memoryless model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

The Generalized Falk Method (GFM) for coordinate transformation, together with two model-reduction strategies based on this method, are presented for efficient coupled field-circuit simulations. Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors, called trial vectors, to construct a vector basis for coordinate transformation. The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems. We also show that, unlike the Pad´e-via-Lanczos (PVL) method, the GFM does not generate unstable positive poles while reducing the order of circuit problems. Further, the proposed GFM is also faster when compared to methods of the type Lanczos (or Krylov) that are already widely used in circuit simulations for electrothermal and electromagnetic problems. The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods. Further, we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system. The implementation of these equivalent circuit networks in circuit simulators is discussed. With the proposed model-reduction strategies, significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

42 ENGINEERING↗
DOE OSTI2020

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

Here in this work we present a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.

42 ENGINEERING↗
DOE OSTI2020

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2021

Skeletal model reduction with forced optimally time dependent modes

Skeletal model reduction based on local sensitivity analysis of time dependent systems is presented in which sensitivities are modeled by forced optimally time dependent (f-OTD) modes. The f-OTD factorizes the sensitivity coefficient matrix into a compressed format as the product of two skinny matrices, i.e. f-OTD modes and f-OTD coefficients. The modes create a low-dimensional, time dependent, orthonormal basis which capture the directions of the phase space associated with most dominant sensitivities. These directions highlight the instantaneous active species, and reaction paths. Evolution equations for the f-OTD modes and coefficients are derived, and the implementation of f-OTD for skeletal reduction is described. For demonstration, skeletal reduction is conducted of the constant pressure ethylene-air burning in a zero-dimensional reactor, and new reduced models are generated. The laminar flame speed, the ignition delay, and the extinction curve as predicted by the models are compared against some existing skeletal models in literature for the same detailed model. Finally, the results demonstrate the capability of f-OTD to eliminate unimportant reactions and species in a systematic, efficient and accurate manner.

42 ENGINEERING↗