Learning noise-induced transitions by multi-scaling reservoir computing

TL;DR

This paper demonstrates that reservoir computing can effectively learn and predict noise-induced transitions in stochastic systems, capturing transition statistics and dynamics from data.

Contribution

It introduces a novel training protocol for reservoir computing to model noise-driven transitions, applicable to various stochastic systems including biological data.

Findings

Accurately predicts transition times and counts in bistable systems.

Effective on systems with white and colored noise, including protein folding.

Captures asymmetry and non-detailed balance effects.

Abstract

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a functional role of driving transitions between stable states underlying many natural and engineered stochastic dynamics. To capture such stochastic transitions from data, we find that leveraging a machine learning model, reservoir computing as a type of recurrent neural network, can learn noise-induced transitions. We develop a concise training protocol for tuning hyperparameters, with a focus on a pivotal hyperparameter controlling the time scale of the reservoir dynamics. The trained model generates accurate statistics of transition time and the number of transitions. The approach is applicable to a wide class of systems, including a bistable system under a double-well potential, with either white noise or colored noise. It is also aware of the asymmetry of the double-well potential, the rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns the transition time between folded states, providing a possibility of predicting transition statistics from a small dataset. The results demonstrate the capability of machine-learning methods in capturing noise-induced phenomena.