Machine Learning of Dynamical Systems: From Chaos to Conservation Laws

Speaker: 张宏坤 (美国麻省大学)

Time: 2025-12-23 10:30-11:30
Location: 1210, SIMIS

Abstract:

We develop a unified machine learning framework for dynamical systems that captures structures ranging from chaos to conservation laws. For chaotic dynamics, we introduce a purely data-driven approach for reconstructing unknown systems, enabling accurate long-term iteration without model priors. For conservative dynamics, we propose trajectory-based learning of Hamiltonian systems that automatically recovers complete conservation structures, including all independent invariants and their involutive relations. We further show that neural network mappings can themselves exhibit chaotic behavior, and establish a theoretical link between parameter perturbations, period–chaos bifurcations, and positive Lyapunov exponents. This work provides a mathematical foundation for learning and analyzing complex dynamical systems.

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About Speaker

Hongkun Zhang, professor at the University of Massachusetts, USA. Her research lies at the intersection of dynamical systems and machine learning, with contributions to chaotic and Hamiltonian dynamics, interpretable system learning, and the theoretical integration of deep learning and dynamics. She has received the NSF CAREER Award, the “Simons Fellowship in Mathematics and Physics”, and the Queensland Ether Raybould Visiting Fellowship.