Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
This work addresses the challenge of inferring dynamics for physical systems, offering potential benefits for model-based control strategies, though it appears incremental as it builds on existing ODE-Net and Hamiltonian dynamics concepts.
The paper tackles the problem of learning Hamiltonian dynamics from observed state trajectories by introducing Symplectic ODE-Net (SymODEN), a deep learning framework that incorporates physics-informed inductive bias to improve generalization with fewer training samples, resulting in interpretable and physically-consistent models for physical systems.
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.