Simulating Fluid Dynamics with a Parameter-Efficient Neural Architecture

Neural operators provide fast surrogates for fluid forecasting, but accurate prediction with a compact model remains challenging. Fluid evolution combines spatial transport with changes in field values, yet many architectures represent both through the same latent transformations, which can increase the representational burden. To address this, we introduce SIDDY, a parameter-efficient neural architecture that reuses observed content through explicit transport and learns a refinement process for the remaining evolution. Specifically, a shared encoder first summarizes the full observation history to guide both transport and refinement, while the latest field supplies the state that is explicitly evolved. Semi-Lagrangian sampling then transports this field once, after which reaction-diffusion layers refine the transported state through learned nonlinear updates and fixed Laplacian stencils. This physics-inspired decomposition enables accurate forecasting with a compact parameterization. Experiments on both simulated and real-world dynamics show that SIDDY achieves the lowest $L_2$ error across all datasets while using only a fraction of the parameters.