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

Rudy Geelen; Laura Balzano; Stephen Wright; Karen Willcox

doi:10.1063/5.0170105

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

Chaos. 2024 Mar 1;34(3):033122. doi: 10.1063/5.0170105.

Authors

Rudy Geelen¹, Laura Balzano², Stephen Wright³, Karen Willcox¹

Affiliations

¹ Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA.
² Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, Michigan 48109, USA.
³ Computer Sciences Department, University of Wisconsin, Madison, Wisconsin 53706, USA.

PMID: 38470262
DOI: 10.1063/5.0170105

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.