Here 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.
Geelen, Rudy, et al. "Learning physics-based reduced-order models from data using nonlinear manifolds." Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 34, no. 3, Mar. 2024. https://doi.org/10.1063/5.0170105
Geelen, Rudy, Balzano, Laura, Wright, Stephen, et al., "Learning physics-based reduced-order models from data using nonlinear manifolds," Chaos: An Interdisciplinary Journal of Nonlinear Science 34, no. 3 (2024), https://doi.org/10.1063/5.0170105
@article{osti_2340141,
author = {Geelen, Rudy and Balzano, Laura and Wright, Stephen and Willcox, Karen},
title = {Learning physics-based reduced-order models from data using nonlinear manifolds},
annote = {Here 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.},
doi = {10.1063/5.0170105},
url = {https://www.osti.gov/biblio/2340141},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
issn = {ISSN 1054-1500},
number = {3},
volume = {34},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2024},
month = {03}}