---
pretty_name: Three-Body Trajectory Benchmark
tags:
  - physics
  - n-body
  - three-body-problem
  - dynamical-systems
  - gravitational-simulation
  - trajectory-prediction
  - graph-neural-networks
task_categories:
  - time-series-forecasting
---

# 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:

```text
(n_trajectories, 200, 3, 5)
```

The last dimension stores the state of one body:

```text
[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:

```text
(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

```python
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.