Projection, Convection, and Response Correction for Long-Horizon Neural Fluid Simulation

Neural network models accelerate fluid simulation through autoregressive rollouts that feed each forecast into the next prediction, but accumulated errors limit long-horizon accuracy. Complementing unrolling and pushforward training, we introduce Mass Projection (MP) and Scalar Consistency (SC) to couple incompressible velocity prediction with scalar transport. MP enforces exact discrete incompressibility, including on walled domains. SC evolves persistent subcell states with the current and projected velocities, retaining scalar structure within grid cells. Its closed-domain transport conserves scalar amount and preserves bounds independently of learned weights, while diffusion, sources and boundary exchange are included explicitly. Both components are differentiable, allowing scalar errors to train the velocity model. We further propose Response Correction (RC), a post-training method that learns how the trained model would continue from the ground-truth next state and uses the predicted response to correct its forecasts. Across three flows from The Well database, MP+RC lowers full-rollout error in 15 of 18 architecture–training settings. In matched one-step comparisons, MP+RC reduces full-rollout error by 89% on Rayleigh–Bénard convection, and MP+SC by 82% on shear flow.