Acceleration of an algebraic multigrid pressure solver using graph neural networks
This work addresses the computational bottleneck of solving the pressure-Poisson equation in incompressible flow solvers, offering a data-driven approach that improves efficiency on unstructured grids.
The paper introduces a graph neural network-based smoother for algebraic multigrid pressure solvers, achieving wall-clock speedups of 4% to 37% across diverse benchmarks and robust generalization to meshes 128x larger than training.
Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities. This work introduces a data-driven algebraic multigrid (AMG) smoother that uses a modified graph convolutional isomorphism network (GCIN). The graph neural network predicts optimal polynomial coefficients to construct a sparse pseudo-inverse operator across diverse grid topologies. The coefficients are optimized to reduce the residual after each V-cycle iteration. By directly capturing the algebraic structure of the system from the sparse coefficient matrix, the proposed method maintains the solver's linearity while adapting to local anisotropies in unstructured grids. Our framework demonstrates significant performance gains by reducing the number of V-cycles required for a given tolerance and delivering wall-clock speedups from 4% to 37% across diverse benchmarks. Notably, the model exhibits robust generalization by maintaining efficiency on meshes up to 128 times larger than those seen in training, and by accelerating the solver's convergence on unseen industry-relevant problems such as the AirfRANS dataset.