# Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features

arXiv: https://arxiv.org/abs/2404.07703 · HTML: https://mlsanity.com/paper/2404.07703/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 11 Apr 2024.

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

- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Random Fourier Features for Operator-Valued Kernels](https://mlsanity.com/paper/1605.02536/) (2016)
- [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)
- [Symplectic Gaussian Process Regression of Hamiltonian Flow Maps](https://mlsanity.com/paper/2009.05569/) (2020)
- [Nonparametric adaptive control and prediction: theory and randomized algorithms](https://mlsanity.com/paper/2106.03589/) (2021)
- [On Kernel Derivative Approximation with Random Fourier Features](https://mlsanity.com/paper/1810.05207/) (2018)
- [Nonlinear System Identification with Prior Knowledge of the Region of Attraction](https://mlsanity.com/paper/2003.12330/) (2020)
- [Kernel-based models for system analysis](https://mlsanity.com/paper/2110.11735/) (2021)
- [Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2312.09734/) (2023)

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

- [DreamSAC: Learning Hamiltonian World Models via Symmetry Exploration](https://mlsanity.com/paper/2603.07545/) (2026)
- [Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features](https://mlsanity.com/paper/2410.18656/) (2024)

## Abstract (arXiv)

A method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular, odd Hamiltonian vector fields. This is done with a symplectic kernel, and it is shown how the kernel can be modified to an odd symplectic kernel to impose the odd symmetry. A random feature approximation is developed for the proposed odd kernel to reduce the problem size. The performance of the method is validated in simulations for three Hamiltonian systems. It is demonstrated that the use of an odd symplectic kernel improves prediction accuracy and data efficiency, and that the learned vector fields are Hamiltonian and exhibit the imposed odd symmetry characteristics.