2D SMOKE PRESSURE SOLVING USING CUSTOM TRANSFORMER-BASED DEEP NEURAL NETWORK

High-resolution simulation of incompressible smoke is computationally expensive because it requires repeatedly enforcing incompressibility through large Poisson solves while advecting fields that contain fine-scale structure. Although classical Eulerian projection-based solvers are robust and widely used, their cost grows rapidly with grid resolution, making high-fidelity results difficult to achieve in interactive settings. Recent progress in deep learning suggests that expensive numerical operators can be approximated by compact neural surrogates. In this work, we accelerate the pressure projection step in a two-dimensional smoke solver by replacing the iterative Poisson solver with a lightweight neural model. Instead of learning the entire simulation pipeline, we target the dominant linear solve and learn a direct mapping from the divergence of the intermediate velocity field to the corresponding pressure field used for projection. Training data is generated directly from the baseline simulator using its existing discretization and boundary handling, ensuring consistency between supervision and deployment. The proposed network is a multi-scale transformer-based encoder-decoder designed for efficient inference. To preserve physical correctness, training uses a composite objective that combines pressure reconstruction with an operator-level constraint that penalizes violations of the Poisson equation. The learned solver is integrated as a drop-in module within the simulator and supports varying runtime resolutions through interpolation before and after inference. The resulting system provides substantial speed-ups of the projection stage while maintaining visually plausible behavior over the evaluated sequences, enabling faster high-resolution smoke generation without modifying the remaining components of the solver.