发表机构
Amity University Haryana; Nagoya Institute of Technology; Central University of Rajasthan（哈里亚纳阿美蒂大学; 名古屋工业大学; 拉贾斯坦中央大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于参数感知储备池计算（PARC）的机器学习框架，成功预测逻辑映射与耦合映射格（CML）的相序转变，为混沌系统的序参数动力学预测提供了数据驱动方案。
AI 中文摘要
耦合逻辑映射表现出其方向相的集体有序性。随着系统参数变化，方向相可从同相态转变为反相态，而单个映射轨迹仍保持混沌。本研究提出一种基于参数感知储备池计算（PARC）的数据驱动机器学习（ML）框架，用于预测两类代表性系统的序参数动力学：逻辑映射与二维耦合映射格（CML）。对于逻辑映射，储备池仅在分岔参数μ低于吸引子合并危机（μ₀=3.6786）的危机前时间序列上训练，训练后的储备池可重构完整分岔图，并正确预测方向序参数M(μ)在危机点处从有序态（M≈0）到无序态（M≠0）的转变。对于CML，利用格的空间均匀性：单个储备池在一个代表性格点的动力学上训练，预测阶段被复制到所有L²个格点，其中L=50，该复制储备池可正确预测在μ≈3.82处从同相同步（θ≈1）到反相聚类态（θ≈0）的转变，θ量化格点间的相相干性。
英文摘要
Coupled logistic maps exhibit collective ordering of their directional phases. As the system parameter varies, the directional phases can undergo a transition from an in-phase state to an anti-phase state, while the individual map trajectories remain chaotic. In this work, we propose a data-driven machine learning (ML) framework based on parameter-aware reservoir computing (PARC) to predict order-parameter dynamics in two representative systems: a logistic map and a two-dimensional coupled map lattice (CML). For the logistic map, the reservoir is trained using only pre-crisis time series data at bifurcation parameter $μ$ values below the attractor-merging crisis ($μ_0 = 3.6786$). The trained reservoir reconstructs the full bifurcation diagram and correctly predicts the transition in the directional order parameter $M(μ)$, from an ordered state ($M \approx 0$) to a disordered state ($M \neq 0$) across the crisis point. For the CML, we exploit the spatial homogeneity of the lattice: a single reservoir is trained on the dynamics of one representative lattice site and is then replicated across all $L^2$ sites during prediction, where $L$=50. The replicated reservoir correctly predicts the transition from in-phase synchronization ($θ\approx 1$) to anti-phase clustered states ($θ\approx 0$) at $μ\approx 3.82$, where $θ$ quantifies phase coherence across lattice sites.
