Scientific Reports · 2026 · First author
G-PARC: physics-aware graph networks on unstructured meshes
Convolutional PARC only runs on uniform Cartesian grids. G-PARC moves it onto graphs, so it works on the irregular meshes that engineering simulations actually use, including meshes that move as a structure deforms. Spatial derivatives come from moving least squares (MLS) kernels on the mesh stencil, and a numerical integrator advances the state.
- 604–2,382×
- higher throughput than neural-operator baselines (GINO, GNO)
- Any Δt
- one trained model handles arbitrary timesteps at inference
- 3 domains
- elastoplastic impact, planar shock waves, river flood forecasting
Architecture · differentiate, then integrate
- x(t) node and edge state on the mesh
-
GATConv
learned featuresMLS operators
∇ · ∇² · strain - SPADE + FiLM fuse physics, condition on Δt
- ∂x/∂t → RK4 · Heun · Euler
- x(t + Δt)↺ repeat for each step of the rollout