Sparse Identification of Slow Timescale Dynamics

TL;DR

This paper introduces a novel method to accurately extract slow timescale dynamics from multiscale signals by combining clustering, dynamic mode decomposition, and sparse regression, enabling the discovery of underlying slow evolution equations.

Contribution

It presents a new approach that leverages averaging, clustering, and sparse regression to identify slow scale dynamics from multiscale data, which was previously challenging.

Findings

Effective extraction of slow dynamics from multiscale signals

Method accurately discovers continuous-time slow evolution equations

Applicable to signals with well-separated timescales

Abstract

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the emergent slow scale evolution is unknown. Yet the course-grained, slow scale dynamics is often of greatest interest in practice. In this work we present an accurate and efficient method for extracting the slow timescale dynamics from signals exhibiting multiple timescales that are amenable to averaging. The method relies on tracking the signal at evenly-spaced intervals with length given by the period of the fast timescale, which is discovered using clustering techniques in conjunction with the dynamic mode decomposition. Sparse regression techniques are then used to discover a mapping which describes iterations from one data point to the next. We show that for sufficiently disparate timescales this discovered mapping can be used to discover the continuous-time slow dynamics, thus providing a novel tool for extracting dynamics on multiple timescales.