高阶结构在储层计算中的应用与改进
Application and Improvement of High-Order Structures in Reservoir Computing
DOI: 10.12677/IJM.2026.151003, PDF,   
作者: 刘超强：浙江师范大学数学科学学院，浙江 金华
关键词: 储层计算；机器学习；邻域多项式库；Reservoir Computing； Machine Learning； Neighboring Polynomial Library
摘要: 高阶结构在预测非线性和混沌动力系统的状态演化方面对储层计算起着至关重要的作用。文章基于多项式储层理论和局部特征提取理论，并借鉴图神经网络（GNNs）通过聚合节点邻域信息来更新节点状态的有效性，提出了一种具有高阶结构的改进储层计算方法。该方法引入了邻域多项式的概念，并通过基于储层状态向量构建邻域多项式库，更科学地扩展了储层特征空间，以捕捉更复杂的非线性关系，从而增强了模型的表示能力。研究采用Lorenz-63系统、Lorenz-96系统和Kuramoto-Sivashinsky系统对其有效性进行了验证。本研究使计算储层模型能够更好地处理复杂的非线性问题，为时间序列预测、模式识别和动态系统分析提供了更强大的工具。
Abstract: High-order structures play a crucial role in reservoir computing for predicting state evolution in nonlinear and chaotic dynamical systems. This study proposes an improved method for higher-order structure reservoir computing based on polynomial reservoir theory and local feature extraction theory, as well as the effectiveness of graph neural networks (GNNs) in updating the state of nodes by aggregating their neighborhood information. The method introduces the concept of neighborhood polynomials and extends the reservoir feature space more scientifically by constructing a library of neighborhood polynomials based on reservoir state vectors to capture more complex nonlinear relationships, thereby enhancing the model’s representation capability. We validate its effectiveness using the Lorenz-63 system, Lorenz-96 system, and Kuramoto-Sivashinsky system. This research enables computational reservoir models to better handle complex nonlinear problems, providing more powerful tools for time series prediction, pattern recognition, and dynamical system analysis.
文章引用：刘超强. 高阶结构在储层计算中的应用与改进[J]. 力学研究, 2026, 15(1): 19-34. https://doi.org/10.12677/IJM.2026.151003

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