This repository contains the code for the paper:

• Symplectic Spectrum Gaussian Processes: Learning Hamiltonians from Noisy and Sparse Data

In this work, we present a Gaussian process that incorporates the symplectic geometric structure of Hamiltonian systems, which is used as a prior distribution for estimating Hamiltonian systems with additive dissipation. Experiments on several physical systems show that the proposed model offers excellent performance in predicting dynamics that follow the energy conservation or dissipation law from noisy and sparse data.

This code is written in Python 3, and depends on PyTorch and torchdiffeq. Only the executable file is written in Ruby 3.

• To obtain the datasets of several physical systems (Pendulum, Duffing Oscillator, Double Pendulum), please enter the following command in data.

ruby run.rb

• Then, one can reproduce our results by the following command in model.

ruby run.rb

Results are stored in data/[system]/.

@inproceedings{tanaka2022,
	title={Symplectic Spectrum Gaussian Processes: Learning Hamiltonians from Noisy and Sparse Data},
	author={Yusuke Tanaka and Tomoharu Iwata and Naonori Ueda},
	booktitle={Advances in Neural Information Processing Systems},
	year={2022}
	}