Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computing

TL;DR

This paper introduces a hybrid reservoir computing approach that combines analytical models with data-driven methods to improve surrogate modeling of nonlinear oscillator networks, especially under model inaccuracies.

Contribution

The study demonstrates that hybrid reservoir computing outperforms standard methods and is more robust to parameter variations, effectively capturing complex dynamics even with incomplete models.

Findings

Hybrid reservoir computers outperform standard reservoirs.

Hybrid models are more robust to parameter tuning.

Performance remains stable across spectral radius thresholds.

Abstract

Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir computing with "expert" analytical models. Simulating the absence of an exact model, we first test the surrogate models with parameter errors in their expert model. Second, in a residual physics task, we assess their performance when their expert model lacks key non-linear coupling terms present in an extended ground-truth model. We focus on short-term forecasting across diverse dynamical regimes, evaluating the use of these surrogates for control applications. We show that hybrid reservoir computers generally outperform standard reservoir computers and exhibit greater robustness to parameter tuning. This advantage is less pronounced in the residual physics task. Notably, unlike standard reservoir computers, the performance of the hybrid does not degrade when crossing an observed spectral radius threshold. Furthermore, there is good performance for dynamical regimes not accessible to the expert model, demonstrating the contribution of the reservoir.