Brief

Researchers have developed a novel data-driven smoother for algebraic multigrid (AMG) pressure solvers, utilizing a modified graph convolutional isomorphism network (GCIN). This graph neural network predicts optimal polynomial coefficients to construct a sparse pseudo-inverse operator, effectively capturing the algebraic structure of the system and adapting to local anisotropies in unstructured grids. The approach demonstrated significant performance improvements, reducing V-cycles and achieving wall-clock speedups of 4% to 37% across various benchmarks. Notably, the model showed robust generalization capabilities, maintaining efficiency on meshes significantly larger than those used in training and accelerating convergence on industry-relevant problems. AI

Researchers have developed RAPNet, a novel graph neural network (GNN) framework designed to accelerate algebraic multigrid (AMG) solvers. This framework addresses the challenge of balancing sparsity and convergence quality in coarse-grid operators, a common issue with classical AMG methods. RAPNet learns to generate sparse, robust coarse operators directly from the algebraic system, utilizing a level-wise training strategy for effective generalization across large domains. The method operates during the solver setup phase, preserving the efficiency of the solve phase and outperforming traditional baselines on various scientific computing tasks. AI