TY - JOUR
T1 - AutoAMG($θ$): An Auto-Tuned AMG Method Based on Deep Learning for Strong Threshold
AU - Zou , Haifeng
AU - Xu , Xiaowen
AU - Zhang , Chen-Song
AU - Mo , Zeyao
JO - Communications in Computational Physics
VL - 1
SP - 200
EP - 220
PY - 2024
DA - 2024/07
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0072
UR - https://global-sci.org/intro/article_detail/cicp/23301.html
KW - AMG, strong threshold, graph neural network, auto-tuning, multiscale matrix.
AB - <p style="text-align: justify;">Algebraic Multigrid (AMG) is one of the most widely used iterative algorithms for solving large sparse linear equations $Ax=b.$ In AMG, the coarse grid is a
key component that affects the efficiency of the algorithm, the construction of which
relies on the strong threshold parameter $θ.$ This parameter is generally chosen empirically, with a default value in many current AMG solvers of 0.25 for 2D problems and
0.5 for 3D problems. However, for many practical problems, the quality of the coarse
grid and the efficiency of the AMG algorithm are sensitive to $θ;$ the default value is
rarely optimal, and sometimes is far from it. Therefore, how to choose a better $θ$ is
an important question. In this paper, we propose a deep learning based auto-tuning
method, AutoAMG($θ$) for multiscale sparse linear equations, which are common in
practical problems. The method uses Graph Neural Network (GNN) to extract matrix features, and a Multilayer Perceptron (MLP) to build the mapping between matrix
features and the optimal $θ,$ which can adaptively predict $θ$ values for different matrices. Numerical experiments show that AutoAMG($θ$) can achieve significant speedup
compared to the default $θ$ value.</p>