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Poster
Learning Algebraic Multigrid Using Graph Neural Networks
Ilay Luz · Meirav Galun · Haggai Maron · Ronen Basri · Irad Yavneh

Tue Jul 14 09:00 AM -- 09:45 AM & Tue Jul 14 10:00 PM -- 10:45 PM (PDT) @ Virtual #None

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator---a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.

Author Information

Ilay Luz (Weizmann Institute of Science)
Meirav Galun (Weizmann Institute of Science)
Haggai Maron (NVIDIA Research)

I am a Research Scientist at NVIDIA Research. My main fields of interest are machine learning, optimization, and shape analysis. More specifically, I am working on applying deep learning to irregular domains (e.g., graphs, point clouds, and surfaces) and graph/shape matching problems. I completed my Ph.D. in 2019 at the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman.

Ronen Basri (Weizmann Institute of Science)
Irad Yavneh (Technion)

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