Speaker
Description
The numerical integration of Hamiltonian systems is a central topic in computational physics and theoretical chemistry. Intrinsic structure-preserving symplectic networks (SympNets) [1] are a widely used tool when it comes to learning symplectic integrators for Hamiltonian systems from data. More often then not Hamiltonian systems of interest depend on a set of parameters. Currently, SympNets do not respect parameters. Therefore, SympNets have to be retrained for every new parameter combination. To eliminate this necessity, we propose to extend the SympNet architecture to handle parameters explicitly, making it suitable for parametric Hamiltonian systems. This approach is coined ”ParSympNets”. We perform different numerical experiments to investigate the approximation and generalization capabilities of ParSympNets. Furthermore, we present a new universal approximation theorem, which shows that ParSympNets can approximate arbitrary parametric symplectic maps.
References
[1] P. Jin, Z. Zhang, A.Zhu, Y. Tang, and G. E. Karniadakis., SympNets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian system, Neural Networks, 132:166–179, 2020.
