CGDT-CESN: Correlation-Guided and Dynamics-Trained Clustered Echo State Network for Multivariate Time-Series Prediction

Accurate prediction of multivariate time series requires models that simultaneously capture variable-specific dynamics and cross-variable interactions. In this work, a Correlation-Guided and Dynamics-Trained Clustered Echo State Network (CGDT-CESN) is proposed, which comprises a modular reservoir architecture with each cluster distinctly specializing in one of the variables in the multivariate time series.

准确预测多变量时间序列需要能够同时捕捉特定变量动态和跨变量交互的模型。在这项工作中，提出了一种相关性引导和动态训练的聚类回声状态网络（CGDT-CESN），它包含一种模块化储备池架构，其中每个聚类专门针对多变量时间序列中的一个变量。

An innovative reservoir design is proposed in which inter-cluster connections are enabled by empirically observed correlations among variables, providing a data-driven coupling mechanism. Apart from conventional readout training, inter-cluster connection weights informed by correlations are trained, which in turn allows the reservoir to capture time-varying cross-variable dependencies without sacrificing computational efficiency and further improves forecasting accuracy.

文中提出了一种创新的储备池设计，通过变量间经验观察到的相关性来启用聚类间连接，从而提供了一种数据驱动的耦合机制。除了传统的读出训练外，还对基于相关性的聚类间连接权重进行了训练，这使得储备池能够在不牺牲计算效率的情况下捕捉随时间变化的跨变量依赖关系，并进一步提高了预测精度。

The prediction performance of CGDT-CESN is found to be superior to that of the conventional ESN when evaluated on two fundamentally different datasets: Twitter information cascade evolution and solar wind forecasting. Also, the improvement in performance is preserved across multiple prediction horizons, even when presented with a low volume of data.

在两个本质上不同的数据集（Twitter信息级联演化和太阳风预测）上进行评估时，CGDT-CESN的预测性能被发现优于传统的ESN。此外，即使在数据量较少的情况下，这种性能提升在多个预测视界中依然保持。

By unifying cluster-specific specialization with learned inter-variable coupling, CGDT-CESN offers a principled, data-driven route to multivariate time series prediction.

通过将特定聚类的专业化与学习到的变量间耦合相结合，CGDT-CESN为多变量时间序列预测提供了一种原则性的、数据驱动的途径。