Learning Hamiltonian dynamics with reservoir computing

Reconstructing the KAM dynamics diagram of Hamiltonian system from time series a limited number parameters is an outstanding question in nonlinear science, especially when governing are unknown. Here, we demonstrate that this can be addressed by machine learning approach knowing as reservoir computer (RC). Specifically, show without prior knowledge about Hamilton's equations motion, trained RC able to not only predict short-term evolution state, but also replicate long-term ergodic properties dynamics. Furthermore, architecture parameter-aware RC, acquired at handful reconstruct entire with high precision tuning control parameter externally. The feasibility and efficiency techniques demonstrated two classical systems, namely double-pendulum oscillator standard map. Our study indicates that, complex dynamical system, learn data Hamiltonian.