Predicting multi-parametric dynamics of externally forced oscillators using reservoir computing and minimal data

Abstract

Mechanical systems are known to exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness, and also due to changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the trained external forcing, but it also manages to provide qualitatively accurate and robust system response predictions for completely unknown \textit{multi-}parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework can correctly predict higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.