Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
Authors: Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty
Keywords: Deep Model Learning, Physics-based Priors, Control of Mechanical Systems
TL;DR: This work enforces Hamiltonian dynamics with control to learn system models from embedded position and velocity data, and exploits this physically-consistent dynamics to synthesize model-based control via energy shaping.
Abstract: In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.