• Open Access

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

Jordan Snyder, Anatoly Zlotnik, and Andrey Y. Lokhov
Phys. Rev. Research 2, 043402 – Published 22 December 2020

Abstract

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.

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  • Received 28 September 2020
  • Accepted 4 December 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043402

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsNetworks

Authors & Affiliations

Jordan Snyder1,2,*, Anatoly Zlotnik3, and Andrey Y. Lokhov3

  • 1Department of Mathematics, University of California, Davis, California 95616, USA
  • 2Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
  • 3Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *jsnyd@uw.edu

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Issue

Vol. 2, Iss. 4 — December - December 2020

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