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    Machine learning prediction of explosive death in coupled oscillator networks

    Zhonghua Zhang1,2, Liang Wang1,*, Xinyi Li1, Ludovico Minati3,4, Michael Small5, Stefano Boccaletti3,6,7,2,†, and Wei Xu1

    • *Contact author: liangwang1129@nwpu.edu.cn
    • †Contact author: stefano.boccaletti@gmail.com

    Phys. Rev. E 114, 054207 – Published 4 November, 2026

    DOI: https://doi.org/10.1103/l51k-63y5

    Abstract

    The accurate prediction of first-order phase transitions such as explosive death is essential for preventing irreversible dynamical collapse in complex networks. Many existing approaches struggle to scale to high-dimensional networks and to identify critical transitions driven by parameter variations. This work introduces a parameter-aware parallel reservoir computing (PPRC) framework, where control parameters serve as additional inputs into a nodewise reservoir architecture. This design enables efficient prediction of dynamics in large-scale networks and remains sensitive to parameter variations. The framework is trained using bidirectional parameter scanning data, establishing separate forward and backward parameter-aware models that effectively capture the hysteresis loop of phase transitions. We validate the PPRC framework on three representative oscillator networks with distinct network topologies, including a nearest-neighbor ring and small-world and random regular graphs. The results demonstrate that PPRC accurately identifies abrupt dynamical transitions, such as explosive amplitude death and oscillation death. Specifically, PPRC captures the associated hysteresis and reconstructs spatiotemporal patterns across the network under unseen parameters. PPRC can also accommodate unknown network connectivity through data-driven topology inference. This work presents an efficient machine learning approach for predicting abrupt transitions in complex systems.

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