Hignn Suspension Eval

hignn-suspension-eval

Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network — Ma et al. (2022) (arXiv:2206.13905, 2022)

What this evaluates

Evaluates a graph neural network's ability to predict particle velocities in particulate suspensions by learning many-body hydrodynamic interactions. It probes transferability across particle counts, external forcing types, and domain boundaries, alongside computational efficiency.

Datasets

• HIGNN-Training-Data — total 80000; splits: train (60000), test (20000)

Metrics

• loss (primary) — range: other
  • Mean squared error between the HIGNN-predicted particle velocities and the ground-truth velocities computed via Stokesian Dynamics (SD). Minimized during training and reported for validation.

Input / output format

Input: 3D relative positions of particles, inter-particle distances, and applied 3D force vectors for each particle.

Output: 3D velocity vector for each particle.

Scoring recipe

def compute_loss(pred_velocities, true_velocities):
    # pred_velocities, true_velocities: shape (N_particles, 3)
    return np.mean((pred_velocities - true_velocities) ** 2)

Common pitfalls

• The model is trained exclusively on 3-particle configurations but evaluated on systems with 4 to 1,600 particles, relying on architectural transferability rather than retraining.
• Ground truth velocities are generated using Stokesian Dynamics (SD) simulations, which contain numerical approximations rather than exact analytical solutions.
• Evaluation focuses on specific lattice structures and Morse potential forces, so performance on arbitrary random particle arrangements may differ.

Evidence (verbatim from paper)

The generated data were then used to train the HIGNN by minimizing the loss given in Eq. (5). When generating data and training the HIGNN, without assuming any prior knowledge we set a sufficiently long cutoff R_cut=20.0 for the three-body contributions and thereby for building the face connectivity in the graph.

Citation

@misc{ma2022fast,
  title={Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network},
  author={Ma et al. (2022)},
  year={2022},
  note={arXiv:2206.13905}
}

• arXiv: 2206.13905