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arXiv · 2308.02802

Learning physics-based reduced-order models from data using nonlinear manifolds

Rudy Geelen·Laura Balzano·Stephen Wright·Karen Willcox
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Abstract

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

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Rudy Geelen, Laura Balzano, Stephen Wright, Karen Willcox. 2023-08-05. Learning physics-based reduced-order models from data using nonlinear manifolds. https://doi.org/10.1063/5.017010

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