这篇论文用图神经网络优化AMG求解器，在非结构网格上提速最高37%，而且能在128倍大的网格上照样用，搞CFD的可以看看。
本研究提出一种数据驱动的代数多重网格（AMG）平滑器，采用改进的图卷积同构网络（GCIN）。该网络从稀疏系数矩阵中学习最优多项式系数，以构建稀疏伪逆算子，在非结构化网格上减少V-cycle迭代次数。在多个基准测试中，该方法实现了4%到37%的壁钟时间加速。模型展现出强大的泛化能力，可处理训练时未见过的、尺寸大128倍的网格，并加速AirfRANS数据集等工业相关问题的收敛。
Acceleration of an algebraic multigrid pressure solver using graph neural networks
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.