# Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features

arXiv: https://arxiv.org/abs/2410.18656 · HTML: https://mlsanity.com/paper/2410.18656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [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 Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning](https://mlsanity.com/paper/1608.05639/) (2016)
- [Nonparametric adaptive control and prediction: theory and randomized algorithms](https://mlsanity.com/paper/2106.03589/) (2021)
- [Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2312.09734/) (2023)
- [Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features](https://mlsanity.com/paper/2404.07703/) (2024)

## Abstract (arXiv)

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.