Data-driven Selection of Coarse-Grained Models of Coupled Oscillators

TL;DR

This paper presents a data-driven method for deriving coarse-grained models of coupled oscillators, enabling simplified yet accurate representations of complex multi-scale dynamical systems.

Contribution

It introduces an optimization-based approach to infer effective reduced models for heterogeneous oscillator populations, expanding the toolkit for multi-scale system analysis.

Findings

Optimized coarse-grained models accurately capture system dynamics.

Method allows for diverse functional forms with comparable accuracy.

Provides a systematic way to derive reduced models from data.

Abstract

Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to obtain using solely analytical methods. Rigorous methodologies for finding such coarse-grained representations of multi-scale phenomena would enable accelerated computational simulations and provide fundamental insights into the complex dynamics of interest. We focus on a heterogeneous population of oscillators of Kuramoto type as a canonical model of complex dynamics, and develop a data-driven approach for inferring its coarse-grained description. Our method is based on a numerical optimization of the coefficients in a general equation of motion informed by analytical derivations in the thermodynamic limit. We show that certain assumptions are required to obtain an autonomous coarse-grained equation of motion. However, optimizing coefficient values enables coarse-grained models with conceptually disparate functional forms, yet comparable quality of representation, to provide accurate reduced-order descriptions of the underlying system.