Abstract
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.
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Data availability
The datasets generated during and/or analysed during the current study are available in the Zenodo repository at the following link: https://doi.org/10.5281/zenodo.18504260.
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Acknowledgements
This work was supported by Key R&D Program Projects in Xinjiang Autonomous Region, China (No. 2023B01032) and Research Project of Xinjiang Sky-Ground Integrated Intelligent Computing Technology Laboratory, China (No. 2025A05-1) and the Tianshan Talent Training Project-Xinjiang Science and Technology Innovation Team Program, China (No. 2023TSYCTD0012).
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S.Z. conceived the study, developed the methodology and software, and wrote the main manuscript text. W.L. validated the results and acquired funding. Z.H.J. reviewed and edited the manuscript and acquired funding. H.W. was responsible for project administration. All authors reviewed the manuscript.
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Zhang, S., Le, W., Jia, ZH. et al. HERA: a Hybrid Euler Reservoir Architecture for multivariate time series classification. Sci Rep (2026). https://doi.org/10.1038/s41598-026-48833-4
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DOI: https://doi.org/10.1038/s41598-026-48833-4
