Lin Zequn, Lu Zhaofan, Di Zengru, Tang Ying
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China.
Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai, 519087, China.
Nat Commun. 2024 Aug 3;15(1):6584. doi: 10.1038/s41467-024-50905-w.
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 computing, 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.
噪声通常被视为不利于从时间序列中提取有效动力学，以至于传统方法通常旨在通过减轻噪声影响来学习动力学。然而，在驱动许多随机动力学所基于的稳定状态之间的转变方面，噪声可能具有功能性作用。我们发现，利用一种机器学习模型——储层计算，能够学习由噪声引起的转变。我们提出了一种简洁的训练协议，重点关注控制时间尺度的关键超参数。该方法具有广泛的适用性，包括具有白噪声或有色噪声的双稳系统，在这种系统中，它能生成白噪声的准确转变时间统计数据以及有色噪声的特定转变时间。相反，诸如稀疏识别非线性动力学（SINDy）和递归神经网络等传统方法，即使对于白噪声情况，也无法如实地捕捉随机转变。本方法还能识别双稳势的不对称性、由非细致平衡引起的旋转动力学以及多稳系统中的转变。对于蛋白质折叠的实验数据，它能学习折叠状态之间的转变时间统计数据，使我们能够从小数据集中表征转变动力学。这些结果预示着将探索扩展从噪声时间序列中学习动力学的主流方法。
