Extending graph network simulators for particle-based simulations of transient flow problems

We extend the Graph Network Simulator (GNS) framework for transient flow problems by treating its processor layer as a tunable design axis. On a common training harness — a six-component physics-informed loss covering acceleration, velocity, position, density, divergence, and vorticity, with dual acceleration/velocity prediction and distributed training with mini-batch noise injection — we evaluate two complementary processor instantiations against vanilla GNS and a non-graph external baseline (the full SFBC pipeline): GNS with the Self-Supervised Graph Attention Operator (GNS-SSGAT), and GNS with a Fourier Basis Convolution layer adapted from SFBC (GNS-FBC). Across two-dimensional lid-driven cavity and curl-noise benchmarks we find that processor choice produces systematically different physical-fidelity profiles, with each instantiation dominating in a different physics regime: GNS-SSGAT achieves the lowest vorticity-field MSE and the highest Pearson correlation on a Material-Point-Method (MPM) semi-compressible regime, while GNS-FBC dominates vorticity-field MSE, Pearson correlation, KL divergence, and long-rollout particle-distribution stability on a harder FLIP/APIC incompressible-liquid regime. Both clearly outperform vanilla GNS and the external SFBC baseline on their respective target regimes, and together they characterize the processor layer as a useful design axis for accurate and stable surrogate modeling of transient flow problems.