In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods are numerical methods used to solve large linear systems of equations efficiently. One of the main differences between AMG methods is how the coarser grid is constructed from a given fine grid. There are two main classes of AMG methods; graph and aggregation based coarsening methods. Here we propose an aggregation-based coarsening framework leveraging graph representation learning and clustering algorithms. Our method introduces the power of machine learning into the AMG research field and opens a new perspective for future researches. The proposed method uses graph representation learning techniques to learn latent features of the graph obtained from the underlying matrix of coefficients. Using these extracted features, we generated a coarser grid from the fine grid. The proposed method is highly capable of parallel computations. Our experiments show that the proposed method's efficiency in solving large systems is closely comparable with other aggregation-based methods, demonstrating the high capability of graph representation learning in designing multi-grid solvers.
RAPNet: Accelerating Algebraic Multigrid with Learned Sparse Corrections
Institute for Interdisciplinary Computational Sciences, Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Be'er Sheva, Israel（交叉学科计算科学研究所，计算机与信息科学学院，内盖夫本·古里安大学，以色列贝尔谢瓦）；Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA（数学与计算机科学系，埃默里大学，美国亚特兰大，GA）
HASSL: Hierarchy-Aware Self-Supervised Learning Framework for Single Cell Microscopy
TUM.ai, Munich, Germany（慕尼黑工业大学人工智能中心，德国慕尼黑）；Ludwig-Maximilian-University, Munich, Germany（慕尼黑大学，德国慕尼黑）；Technical University of Munich, Munich, Germany（慕尼黑工业大学，德国慕尼黑）；Institute of Stem Cell Research, Helmholtz Munich, German Research Center for Environmental Health, Neuherberg, Germany（干细胞研究所，亥姆霍兹慕尼黑中心，德国环境健康研究中心，德国新赫伯格）；Computational Health Center, Helmholtz Munich - German Research Center for Environmental Health, Neuherberg, Germany（计算健康中心，亥姆霍兹慕尼黑中心 - 德国环境健康研究中心，德国新赫伯格）；Department of Medicine III, Ludwig-Maximilian-University Hospital, Munich, Germany（医学部III，慕尼黑大学医院，德国慕尼黑）；Department of Physics, Ludwig-Maximilian-University, Munich, Germany（物理系，慕尼黑大学，德国慕尼黑）；German Cancer Consortium (DKTK), partner site Munich, Germany（德国癌症联盟（DKTK），慕尼黑合作站点，德国慕尼黑）；Munich Center for Machine Learning (MCML), Munich, Germany（慕尼黑机器学习中心（MCML），德国慕尼黑）
Parallel Energy-Minimization Prolongation for Algebraic Multigrid
Department ICEA, University of Padova（帕多瓦大学ICEA学院）；Department of Mathematics and Statistics, University of New Mexico（新墨西哥大学数学与统计系）；Siebel Center for Computer Science, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校西贝尔计算机科学中心）
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Science and Technology Facilities Council, Scientific Computing Department, Rutherford Appleton Laboratory（英国科学与技术设施委员会，科学计算部，卢瑟福阿普尔顿实验室）
Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems
University of Delaware（特拉华大学）；University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校）；University of Crete（克里特大学）；Foundation of Research and Technology-Hellas（希腊研究与技术基金会）
