Data-driven selection of coarse-grained models of coupled oscillators

• Published in: Physical review research Vol. 2; no. 4; p. 043402
• Main Authors: Snyder, Jordan, Zlotnik, Anatoly, Lokhov, Andrey Y.
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 22.12.2020
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.2.043402

Systematic discovery of reduced-order closure models for multiscale 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 multiscale 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.