Learning noise-induced transitions by multi-scaling reservoir computing
Zequn Lin Zhaofan Lu Zengru Di Ying Tang
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.