A Review of Data-Driven Discovery for Dynamic Systems

TL;DR

This paper reviews data-driven methods for discovering the underlying equations of complex nonlinear dynamic systems, highlighting approaches, frameworks, and future research directions in the field.

Contribution

It provides a comprehensive categorization and a unified mathematical framework for data-driven discovery methods, integrating statistical perspectives and outlining future research avenues.

Findings

Categorization of data-driven discovery approaches

Unified mathematical framework linking different methods

Discussion on the role of statistics in the field

Abstract

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations driving these complex nonlinear dynamic system using data-driven approaches. In this paper we review the current literature on data-driven discovery for dynamic systems. We provide a categorization to the different approaches for data-driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data-driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework, and provide avenues for future work.