System Identification of Large-Scale Coupled Dynamics Using Differentiable Programming

Abstract

Synchronized nonlinear dynamical systems underpin a wide range of phenomena, from lasers to brainwaves to traffic. Nonlinear ODEs describe these dynamics well in simplified regimes, but they remain challenging to scale to real-world, high-dimensional data. The Kuramoto model for coupled oscillatory systems is a good example, as it has been widely applied, yet performing system identification remains challenging [1,6]. Maximum likelihood estimation (MLE) has shown promise for Kuramoto parameter estimation [5] but requires specialized implementation and remains challenging to apply to real data. We address this gap by using differentiable programming [4] as a new paradigm to scale system identification of the Kuramoto model to high dimensions. We show in synthetic data that our algorithm compares favorably to maximum-likelihood (MLE) estimation, with significantly improved noise and time-scale invariance. This suggests that the differentiable programming approach can be expanded to the study of other nonlinear dynamical systems applied to real-world data.