DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)
This addresses the problem of accelerating computational fluid dynamics simulations for engineers and researchers, though it appears incremental as it builds on existing GNN and physics-informed methods.
The paper tackles solving Poisson problems with mixed boundary conditions on unstructured grids for faster CFD simulations by proposing a deep statistical graph Poisson solver that uses Graph Neural Networks to enforce boundary conditions and minimize the residual directly, achieving results without needing exact solutions.
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing boundary conditions by design. By directly minimizing the residual of the Poisson equation, the model attempts to learn the physics of the problem without the need for exact solutions, in contrast to most previous data-driven processes where the distance with the available solutions is minimized.