Anticipating measure synchronization in coupled Hamiltonian systems with machine learning

A model-free approach is proposed for anticipating the occurrence of measure synchronization in coupled Hamiltonian systems. Specifically, by the technique of parameter-aware reservoir computing in machine learning, we demonstrate that the machine trained by the time series of coupled Hamiltonian systems at a handful of coupling parameters is able to predict accurately not only the critical coupling for the occurrence of measure synchronization, but also the variation of the system order parameters around the transition point. The capability of the model-free technique in anticipating measure synchronization is exemplified in Hamiltonian systems of two coupled oscillators and also in a Hamiltonian system of three globally coupled oscillators where partial synchronization arises. The studies pave a way to the model-free, data-driven analysis of measure synchronization in large-size Hamiltonian systems.