Speaker
Description
Noise is usually regarded as adversarial to extracting effective dynamics from
time series, such that conventional approaches usually aim at learning
dynamics by mitigating the noisy effect. However, noise can have a functional
role in driving transitions between stable states underlying many stochastic
dynamics. We find that leveraging a machine learning model, reservoir com
puting, can learn noise-induced transitions. We propose a concise training
protocol with a focus on a pivotal hyperparameter controlling the time scale.
The approach is widely applicable, including a bistable system with white noise.
or colored noise, where it generates accurate statistics of transition time for
white noise and specific transition time for colored noise. Instead, the conventional approaches such as SINDy and the recurrent neural network do not
faithfully capture stochastic transitions even for the case of white noise. The
present approach is also aware of asymmetry of the bistable potential, rotational dynamics caused by non-detailed balance, and transitions in multi-stable
systems. For the experimental data of protein folding, it learns statistics of
transition time between folded states, enabling us to characterize transition
dynamics from a small dataset. The results portend the exploration of
extending the prevailing approaches in learning dynamics from noisy time
series.
