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

<p>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 title="Paper" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4555181" target="_blank" rel="noopener">A Generalized Framework of Neural Networks for Hamiltonian Systems</a>.</p> <p>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 <a title="Brutus" href="https://comp-astrophys-cosmol.springeropen.com/articles/10.1186/s40668-014-0005-3" target="_blank" rel="noopener">Brutus</a>.</p> <p>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 <a title="Pandas" href="https://pandas.pydata.org/" target="_blank" rel="noopener">Pandas</a> 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.</p> <p>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.</p> <p>The code used to train various neural network architectures on this data can be found on GitHub at: <a title="Code" href="https://github.com/AELITTEN/GHNN" target="_blank" rel="noopener">https://github.com/AELITTEN/GHNN</a>.</p> <p>Already trained neural networks can be found on GitHub at: <a title="NeuralNets_GHNN" href="https://github.com/AELITTEN/NeuralNets_GHNN" target="_blank" rel="noopener">https://github.com/AELITTEN/NeuralNets_GHNN</a>.</p> <table> <tbody> <tr> <td>&nbsp;</td> <td><strong>Single pendulum</strong></td> <td><strong>Double pendulum</strong></td> <td><strong>3-body problem</strong></td> </tr> <tr> <td>Number of trajectories</td> <td>500</td> <td>2000</td> <td>5000</td> </tr> <tr> <td>final time in all_runs</td> <td>T (one period of the pendulum)</td> <td>10</td> <td>10</td> </tr> <tr> <td>final time in training data</td> <td>0.25*T</td> <td>5</td> <td>5</td> </tr> <tr> <td>step size in training data</td> <td>0.1</td> <td>0.1</td> <td>0.5</td> </tr> </tbody> </table> <p>&nbsp;</p>