One-shot prediction of noise-induced bifurcations with reservoir computing

Abstract: Dynamical systems can exhibit complex responses when noise is injected. In particular, dynamics can be qualitatively altered by dynamic noise, a phenomenon known as noise-induced bifurcation. Predicting noise-induced bifurcations is a critical challenge in nonlinear physics. Recently, it has been reported that reservoir computing, a machine learning framework, can reconstruct the unseen global structure of a dynamical system, including bifurcations, from limited time series data. However, learning global structures in random dynamical systems has not yet been systematically addressed. In this study, we report that a simple reservoir computing framework can predict the noise-induced bifurcation structure from the time series at a single noise condition. We demonstrate dynamic noise cancellation and the reconstruction of entire noise-induced bifurcation structures, including noise-induced chaos and noise-induced order, in representative dynamical systems. Additionally, we provide a theoretical explanation for noise cancellation and demonstrate noise cancellation of a neuromorphic spintronics device. Our results provide significant insights into understanding and harnessing real-world noisy complex dynamics.