Li Xin, Zhu Qunxi, Zhao Chengli, Qian Xuzhe, Zhang Xue, Duan Xiaojun, Lin Wei
College of Science, National University of Defense Technology, Changsha, Hunan 410073, China.
Research Institute of Intelligent Complex Systems and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China.
Research (Wash D C). 2023 Jul 3;6:0174. doi: 10.34133/research.0174. eCollection 2023.
Detection in high fidelity of tipping points, the emergence of which is often induced by invisible changes in internal structures or/and external interferences, is paramountly beneficial to understanding and predicting complex dynamical systems (CDSs). Detection approaches, which have been fruitfully developed from several perspectives (e.g., statistics, dynamics, and machine learning), have their own advantages but still encounter difficulties in the face of high-dimensional, fluctuating datasets. Here, using the reservoir computing (RC), a recently notable, resource-conserving machine learning method for reconstructing and predicting CDSs, we articulate a model-free framework to accomplish the detection only using the time series observationally recorded from the underlying unknown CDSs. Specifically, we encode the information of the CDS in consecutive time durations of finite length into the weights of the readout layer in an RC, and then we use the learned weights as the dynamical features and establish a mapping from these features to the system's changes. Our designed framework can not only efficiently detect the changing positions of the system but also accurately predict the intensity change as the intensity information is available in the training data. We demonstrate the efficacy of our supervised framework using the dataset produced by representative physical, biological, and real-world systems, showing that our framework outperforms those traditional methods on the short-term data produced by the time-varying or/and noise-perturbed systems. We believe that our framework, on one hand, complements the major functions of the notable RC intelligent machine and, on the other hand, becomes one of the indispensable methods for deciphering complex systems.
高保真地检测临界点至关重要，因为临界点的出现通常是由内部结构的无形变化或/和外部干扰所引发的，这对于理解和预测复杂动力系统（CDS）非常有益。从多个角度（如统计学、动力学和机器学习）已经成功开发出了检测方法，这些方法各有优势，但在面对高维、波动的数据集时仍会遇到困难。在此，我们使用储层计算（RC）——一种最近备受关注的、资源节约型的用于重建和预测CDS的机器学习方法，阐述了一个无模型框架，该框架仅使用从潜在未知CDS中观测记录的时间序列来完成检测。具体而言，我们将有限长度的连续时间段内CDS的信息编码到RC中读出层的权重中，然后将学习到的权重用作动态特征，并建立从这些特征到系统变化的映射。我们设计的框架不仅可以有效地检测系统的变化位置，而且由于强度信息在训练数据中可用，还能准确预测强度变化。我们使用由代表性物理、生物和现实世界系统产生的数据集证明了我们的监督框架的有效性，表明我们的框架在由时变或/和噪声干扰系统产生的短期数据上优于那些传统方法。我们相信，我们的框架一方面补充了著名的RC智能机器的主要功能，另一方面成为解读复杂系统不可或缺的方法之一。
