# Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control

arXiv: https://arxiv.org/abs/1909.12077 · HTML: https://mlsanity.com/paper/1909.12077/

## Key facts

- Cited by 184 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2019.

## Built on by (most cited first, 30 of 184)

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- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
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- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
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## Abstract (arXiv)

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.