Title: Learning Hamiltonian Dynamics with Machine

Speaker: Dr. Xingang Wang, Professor of Physics, Shaanxi Normal University

Time: June 21, 2022, 10 am – 11 am

Zoom ID: 960 9264 2522

Password: dkumath


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


X.G Wang got his PhD degree from Beijing Normal University in 2002. His PhD thesis is about measure synchronization in coupled Hamiltonian systems, carried out at the Physics Department under the supervision of Prof. Gang Hu. After graduated, he joined the Temasek Laboratories at National University of Singapore as a research scientist, collaborating with Prof. Choy Heng Lai on chaos-based secure communications and complex network analysis. In 2008, he moved back to China and joined the Physics Department at Zhejiang University, working on plasma physics and complex systems. In 2013, he joined Shaanxi Normal University, and now is working in the Physics Department as a “Qujiang” Professor. His current research interest is mainly focusing on the collective dynamical behaviors of complex systems, including synchronization dynamics, pattern formation, complex networks, neuronal networks, machine learning, etc. He has published about 90 peer review papers, which, according to the record of Web of Science, have been cited about 1200 times, with H-index=21.