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Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics

ICML 2024 · Graph learning › GNN architectures · approach: Physics-inspired GNNs · 2 citations (OpenAlex)

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Proposes Neural SPH, which removes external forces from GNN-based simulator targets (with convolution-smoothed forces) and applies SPH relaxation steps at inference to fix particle clustering, improving long rollouts of GNS and SEGNN on seven 2D/3D Lagrangian datasets.

Problem

GNN-based Lagrangian fluid simulators suffer from particle clustering (tensile instability-like artifacts), density violations and unstable long rollouts, and mis-model external forces such as gravity.

Approach

Subtract the accumulated external force from the GNN's learning target (with Gaussian/SPH-kernel smoothing of spatially varying forces), and run a short SPH relaxation (pressure and/or viscous terms, plus a density clipping wall treatment) on the predicted point cloud at inference time without retraining or differentiating through the solver.

Key results

• On 2D DAM, GNS_{g,p} reduces Sinkhorn divergence from 3.8e-2 (GNS) to 7.5e-3 and kinetic energy MSE from 4.6e-2 to 2.1e-3 over 400-step rollouts.
• On 2D LDC, GNS_p reduces MSE_400 from 3.3e-2 to 1.6e-2 and Sinkhorn from 3.1e-4 to 2.8e-7.
• Removing external forces from the GNS target (GNS_g) improves all measures on dam break by at least a factor of 2, up to 5 on the full 400-step rollout.

Measured effects reported in the paper

Surprising findings

• Adding SPH relaxation during training (as regularization) did not improve rollout performance, so relaxation is applied only at inference.
• Removing external force from the target gives worse 20-step position MSE (about 1.5x) on RPF even though long-rollout performance improves.

Limitations

• Relaxation hyperparameters (alpha, beta, loops) require per-dataset tuning and may push learned solver out of distribution.
• External force treatment requires knowledge of the timestep and temporal coarsening level of the dataset.
• Evaluation uses few test trajectories (12-25) after splitting into 400-step sequences, making estimates noisy.

Experimental setup

Datasets: LagrangeBench 2D TGV LagrangeBench 3D TGV LagrangeBench 2D RPF LagrangeBench 3D RPF LagrangeBench 2D LDC LagrangeBench 3D LDC LagrangeBench 2D DAM

Benchmarks: LagrangeBench 2D TGV LagrangeBench 3D TGV LagrangeBench 2D RPF LagrangeBench 3D RPF LagrangeBench 2D LDC LagrangeBench 3D LDC LagrangeBench 2D DAM

Metrics: MSE_400 position error Sinkhorn divergence kinetic energy MSE density MAE Dirichlet energy Chamfer distance

Baselines: GNS SEGNN PDE-Refiner

Builds on: Graph Network-based Simulator LagrangeBench SEGNN PDE-Refiner JAX-SPH

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