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In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learningframework which can infer the dynamics of a physical system, given by anordinary differential equation (ODE), from observed state trajectories. Toachieve better generalization with fewer training samples, SymODEN incorporatesappropriate inductive bias by designing the associated computation graph in aphysics-informed manner. In particular, we enforce Hamiltonian dynamics withcontrol to learn the underlying dynamics in a transparent way, which can thenbe leveraged to draw insight about relevant physical aspects of the system,such as mass and potential energy. In addition, we propose a parametrizationwhich can enforce this Hamiltonian formalism even when the generalizedcoordinate data is embedded in a high-dimensional space or we can only accessvelocity data instead of generalized momentum. This framework, by offeringinterpretable, physically-consistent models for physical systems, opens up newpossibilities for synthesizing model-based control strategies.

Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control