Predict-Project Transformers Perform Stable Large-Scale Particle Simulation Across Hundreds of Autoregressive Timesteps

Simulating free-surface flows with particles is difficult. Particle connectivity changes at every step, and phenomena such as wave propagation emerge only when thousands of particles are coordinated across the whole domain and over hundreds of steps. We find that current learned simulators cannot reproduce these phenomena on core validation scenarios within SPH community. Graph networks are realistic locally but their reach is limited by the receptive range of message passing, while latent-space transformers capture global motion but are bottlenecked by oversmoothing. We also find that no public particle datasets are large enough to clearly measure these failure modes. To address this, we present the Predict-Project Transformer (P2T), which models near-field interactions with message passing and applies a far-field correction with latent attention. On two new datasets built from the SPH community's validation cases, a wave tank and a dam break, P2T is the only model that reproduces the propagating wave and the dam-break impact while keeping particle density close to the reference solver's. Ablations show that its configuration is crucial for rollout stability, and a pre-trained P2T adapts to new tanks, seas and breakers from a handful of simulations. We release the model along with five large-scale datasets.