This dataset includes the code and numerical data to reproduce the results from the paper titled "Symplecticity-Preserving Prediction of Hamiltonian Dynamics by Generalized Kernel Interpolation" (2026). It contains the nonparametric variant, in which the surrogate model is trained for one fixed Hamiltonian system and one prescribed macro time step ΔT; separate surrogate models are trained for different values of ΔT.

Contents

Training data Computed trajectories Reference solutions Fitted surrogate models Error quantities

The data were generated by the provided Python scripts from Hamiltonian test systems and are organized according to the corresponding numerical experiments. The dataset can be used to rerun the experiments, reproduce the figures, and further test structure-preserving kernel surrogate methods.

How to run

Experiment scripts are in the main folder SymplecticKernelApprox, named test*.py Run from a terminal: python <script_name>.py, or start from an IDE (Spyder, PyCharm, VS Code) Supporting functions are in the functions/ subfolder Stored and generated data are in the data/ folder

See the README for more information and installation instructions.