# Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces

arXiv: https://arxiv.org/abs/2312.09734 · HTML: https://mlsanity.com/paper/2312.09734/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Learning Dynamical Systems with Side Information](https://mlsanity.com/paper/2008.10135/) (2020)
- [Contracting Implicit Recurrent Neural Networks: Stable Models with Improved Trainability](https://mlsanity.com/paper/1912.10402/) (2019)
- [Nonparametric adaptive control and prediction: theory and randomized algorithms](https://mlsanity.com/paper/2106.03589/) (2021)
- [Nonlinear System Identification with Prior Knowledge of the Region of Attraction](https://mlsanity.com/paper/2003.12330/) (2020)
- [Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control](https://mlsanity.com/paper/2301.03565/) (2023)

## Built on by (most cited first, 2 of 2)

- [Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features](https://mlsanity.com/paper/2404.07703/) (2024)
- [Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features](https://mlsanity.com/paper/2410.18656/) (2024)

## Abstract (arXiv)

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently Hamiltonian, and where the vector field is required to be odd or even. This is done with a symplectic kernel, and it is shown how this symplectic kernel can be modified to be odd or even. The performance of the method is validated in simulations for two Hamiltonian systems. The simulations show that the learned dynamics reflect the energy-preservation of the Hamiltonian dynamics, and that the restriction to symplectic and odd dynamics gives improved accuracy over a large domain of the phase space.