Model Reduction to Spectral Submanifolds in Non-Smooth Dynamical Systems

TL;DR

This paper introduces a novel model reduction method for non-smooth dynamical systems using spectral submanifolds, enabling low-dimensional, sparse, and nonlinear models that are applicable to both equation-driven and data-driven problems.

Contribution

It develops a new approach to construct reduced models on spectral submanifolds for non-smooth systems, including matching across different smooth regions.

Findings

Effective reduction of non-smooth systems demonstrated

Applicable to both equation-driven and data-driven problems

Models capture essential dynamics with low complexity

Abstract

We develop a model reduction technique for non-smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and non-smooth models on unions of slow and attracting spectral submanifolds (SSMs) for each smooth subregion of the phase space and then properly match them. We apply this methodology to both equation-driven and data-driven problems, with and without external forcing.