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.

翻译：噪声通常被视为从时间序列中提取有效动力学特征的不利因素，因此传统数据驱动方法通常致力于通过抑制噪声效应来学习动力学过程。然而，在众多自然与工程随机动力学中，噪声具有驱动稳定状态间跃迁的功能性作用。为从数据中捕捉此类随机跃迁，我们发现利用机器学习模型——作为递归神经网络类型的储层计算——能够学习噪声诱导的跃迁。我们开发了一套简洁的超参数调优训练协议，重点关注控制储层动力学时间尺度的关键超参数。训练后的模型可生成跃迁时间与跃迁次数的精确统计量。该方法适用于广泛系统，包括双阱势下的双稳系统（含白噪声或色噪声），同时能感知双阱势的非对称性、非细致平衡导致的旋转动力学以及多稳态系统中的跃迁行为。针对蛋白质折叠实验数据，该方法可学习折叠态间的跃迁时间，为从小数据集中预测跃迁统计量提供了可能性。研究结果表明了机器学习方法在捕捉噪声诱导现象方面的能力。