HERA: a Hybrid Euler Reservoir Architecture for multivariate time series classification

Multivariate time series classification (MTSC) is a critical task in fields such as human activity recognition, medical diagnosis, and industrial process monitoring. Its core problem lies in effectively capturing the complex nonlinear dynamics within and between multidimensional variables. Reservoir computing (RC), as an efficient feature extraction model, offers advantages including low computational resource requirements and fast training speeds. However, its performance remains highly dependent on hyperparameter tuning, and standard models may fail to fully leverage the global statistical properties of sequences. In order to address these problems, we propose HERA (Hybrid Euler Reservoir Architecture), a novel classification framework specifically designed for MTSC. At the core of HERA lies an innovative hybrid feature design that synergistically integrates two complementary types of information: (1) Dynamic representations of inter-variable interactions captured by the Euler State Network (EuSN); (2) Static statistical features summarizing the global characteristics of each independent variable. Additionally, the architecture embeds a self-optimization module driven by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to efficiently determine optimal model configurations. Extensive experiments across multiple public MTSC benchmark datasets demonstrate that HERA achieves highly competitive classification accuracy, performing on par with or exceeding various strong baseline models.