  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.
