Li Xueqi, Small Michael, Lei Youming
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.
Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley WA 6009, Australia.
Phys Rev E. 2023 Dec;108(6-1):064304. doi: 10.1103/PhysRevE.108.064304.
The reservoir computing approach utilizes a time series of measurements as input to a high-dimensional dynamical system known as a reservoir. However, the approach relies on sampling a random matrix to define its underlying reservoir layer, which leads to numerous hyperparameters that need to be optimized. Here, we propose a nonlocally coupled pendulum model with higher-order interactions as a novel reservoir, which requires no random underlying matrices and fewer hyperparameters. We use Bayesian optimization to explore the hyperparameter space within a minimal number of iterations and train the coupled pendulums model to reproduce the chaotic attractors, which simplifies complicated hyperparameter optimization. We illustrate the effectiveness of our technique with the Lorenz system and the Hindmarsh-Rose neuronal model, and we calculate the Pearson correlation coefficients between time series and the Hausdorff metrics in the phase space. We demonstrate the contribution of higher-order interactions by analyzing the interaction between different reservoir configurations and prediction performance, as well as computations of the largest Lyapunov exponents. The chimera state is found as the most effective dynamical regime for prediction. The findings, where we present a new reservoir structure, offer potential applications in the design of high-performance modeling of dynamics in physical systems.
储层计算方法利用测量的时间序列作为输入，输入到一个称为储层的高维动力系统中。然而，该方法依赖于对随机矩阵进行采样来定义其底层储层，这导致需要优化众多超参数。在此，我们提出一种具有高阶相互作用的非局部耦合摆模型作为一种新型储层，它不需要随机底层矩阵且超参数较少。我们使用贝叶斯优化在最少的迭代次数内探索超参数空间，并训练耦合摆模型以重现混沌吸引子，这简化了复杂的超参数优化。我们用洛伦兹系统和欣德马什 - 罗斯神经元模型说明了我们技术的有效性，并计算了时间序列之间的皮尔逊相关系数以及相空间中的豪斯多夫度量。我们通过分析不同储层配置之间的相互作用和预测性能以及最大李雅普诺夫指数的计算，证明了高阶相互作用的贡献。发现嵌合体状态是最有效的预测动力状态。我们提出新储层结构的这些发现为物理系统动力学的高性能建模设计提供了潜在应用。
