Flow map data of the singel pendulum, double pendulum and 3-body problem

This dataset was constructed to compare the performance of various neural network architectures learning the flow maps of Hamiltonian systems. It was created for the paper: A Generalized Framework of Neural Networks for Hamiltonian Systems.

The dataset consists of trajectory data from three different Hamiltonian systems. Namely, the single pendulum, double pendulum and 3-body problem. The data was generated using numerical integrators. For the single pendulum, the symplectic Euler method with a step size of 0.01 was used. The data of the double pendulum was also computed by the symplectic Euler method, however, with an adaptive step size. The trajectories of the 3-body problem were calculated by the arbitrarily high-precision code Brutus.

For each Hamiltonian system, there is one file containing the entire trajectory information (*_all_runs.h5.1). In these files, the states along all trajectories are recorded with a step size of 0.01. These files are composed of several Pandas DataFrames. One DataFrame per trajectory, called "run0", "run1", ... and finally one large DataFrame in which all the trajectories are combined, called "all_runs". Additionally, one Pandas Series called "constants" is contained in these files, in which several parameters of the data are listed.

Also, there is a second file per Hamiltonian system in which the data is prepared as features and labels ready for neural networks to be trained (*_training.h5.1). Similar to the first type of files, they contain a Series called "constants". The features and labels are then separated into 6 DataFrames called "features", "labels", "val_features", "val_labels", "test_features" and "test_labels". The data is split into 80% training data, 10% validation data and 10% test data.

The code used to train various neural network architectures on this data can be found on GitHub at: https://github.com/AELITTEN/GHNN.

Already trained neural networks can be found on GitHub at: https://github.com/AELITTEN/NeuralNets_GHNN.

Single pendulum
Double pendulum
3-body problem

Number of trajectories
500
2000
5000

final time in all_runs
T (one period of the pendulum)
10
10

final time in training data
0.25*T
5
5

step size in training data
0.1
0.1
0.5