AlexNeagu123/three-body-trajectory-benchmark

Three-Body Trajectory Benchmark

This dataset contains two-dimensional gravitational three-body trajectories used in a master's thesis on neural prediction of dynamical systems. The benchmark is designed for training and evaluating models that generate future states autoregressively from an initial state.

Each trajectory contains three equal-mass bodies interacting through mutual gravitational interaction. The data were generated with the REBOUND simulation package using the IAS15 integrator. All simulations use gravitational constant G = 1, body mass m = 1, time step dt = 0.05, and 200 sampled states per trajectory.

Files

File	Role	Number of trajectories
train.h5	training split	1000
val.h5	validation split	600
test.h5	test split	600

The validation and test splits are balanced across five trajectory classes defined by the closest encounter reached during the trajectory. The training split follows the same class balance.

State Format

The main dataset inside each HDF5 file is named trajectories and has shape:

(n_trajectories, 200, 3, 5)

The last dimension stores the state of one body:

[x, y, vx, vy, m]

where x, y are planar coordinates, vx, vy are planar velocity components, and m is the body mass.

Each file also contains an energies dataset with shape:

(n_trajectories, 200)

This stores the total mechanical energy of the corresponding trajectory at each sampled time step.

Trajectory Classes

Trajectories are grouped by the minimum pairwise Euclidean distance reached between any two bodies during the full trajectory:

Class	Criterion
close	0.00 <= d_min < 0.02
near	0.02 <= d_min < 0.05
mid	0.05 <= d_min < 0.15
wide	0.15 <= d_min < 0.50
far	0.50 <= d_min

The HDF5 files include the following stratification fields:

Dataset / attribute	Description
encounter_bin_id	integer class id for each trajectory
encounter_bin_name	class name for each trajectory
min_pairwise_distance	minimum pairwise distance for each trajectory
encounter_bins_json	JSON description of the class boundaries

Generation Procedure

Initial positions are sampled from a zero-mean Gaussian distribution with standard deviation 1.0. Initial velocities are sampled from a zero-mean Gaussian distribution with standard deviation 0.5. After sampling, the center-of-mass position and velocity are subtracted so that the generated system does not contain global translation or drift.

Candidate trajectories are rejected if any two bodies approach closer than 10^-3 or if any coordinate leaves the box [-5, 5] x [-5, 5]. Accepted trajectories are then assigned to one of the five trajectory classes according to their minimum pairwise distance.

Loading Example

import h5py

with h5py.File("train.h5", "r") as f:
    trajectories = f["trajectories"][:]          # (1000, 200, 3, 5)
    energies = f["energies"][:]                  # (1000, 200)
    class_names = f["encounter_bin_name"][:]      # (1000,)
    d_min = f["min_pairwise_distance"][:]         # (1000,)

first_state = trajectories[0, 0]                 # (3, 5)

Intended Use

The dataset is intended for studying autoregressive trajectory prediction in gravitational three-body systems. It can be used to compare neural models across both trajectory accuracy and energy conservation, and to analyze how model behavior changes between smooth trajectories and close-encounter trajectories.

The dataset was used in the thesis experiments to train and evaluate E(n)-Equivariant Graph Neural Networks and Hamiltonian Graph Neural Networks under a shared training and evaluation protocol.