Learning noise-induced transitions by multi-scaling reservoir computing.

Area of Science:

• Complex Systems
• Machine Learning
• Time Series Analysis

Background:

• Noise is typically viewed as detrimental to extracting dynamics from time series data.
• Conventional methods often focus on noise reduction, potentially overlooking its functional role in driving system transitions.

Purpose of the Study:

• To investigate the potential of machine learning, specifically reservoir computing, in learning noise-induced transitions.
• To develop an effective training protocol for reservoir computing to capture stochastic dynamics.

Main Methods:

• Utilized reservoir computing, a machine learning technique, to model time series dynamics.
• Developed a concise training protocol focusing on a key hyperparameter for time scale control.
• Applied the method to bistable systems with white and colored noise, and experimental protein folding data.

Main Results:

• Reservoir computing successfully learned noise-induced transitions, outperforming conventional methods like SINDy and recurrent neural networks.
• The approach accurately generated transition time statistics for white noise and specific transition times for colored noise.
• Demonstrated applicability to asymmetric potentials, non-detailed balance dynamics, multi-stable systems, and protein folding dynamics from limited data.

Conclusions:

• Machine learning, particularly reservoir computing, offers a powerful framework for learning dynamics from noisy time series, including noise-induced transitions.
• The proposed method provides a robust tool for analyzing complex stochastic systems and characterizing transition dynamics.
• This work opens avenues for extending existing approaches to dynamics learning in the presence of noise.