Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control

TL;DR

Symplectic ODE-Net (SymODEN) is a deep learning framework that learns Hamiltonian dynamics with control from observed data, incorporating physics-informed inductive bias for better generalization and interpretability.

Contribution

We introduce SymODEN, a novel neural network architecture that enforces Hamiltonian structure with control, enabling transparent and physically consistent modeling of dynamical systems.

Findings

Successfully infers physical system dynamics from limited data.

Enforces Hamiltonian structure even with high-dimensional or velocity-only data.

Provides interpretable models for physical systems and control strategies.

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.