Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

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Machine Learning enhanced Multigrid Methods

Master's Thesis Computer Simulation in Science

Supervision

• Prof. Dr. Matthias Ehrhardt

Description

In this thesis we investigate a new strategy ....

Keywords

Multigrid methods, optimized prolongation operators, optimized restriction operators, efficiency, trainable Multigrid solver, relaxation step, Galerkin coarsening

References:

1. Y. Chen, Bin Dong, J. Xu, Meta-mgnet: Meta multigrid networks for solving parameterized partial differential equations, Journal of Computational Physics 455 (2022): 110996.
2. D. Greenfeld, M. Galun, R. Kimmel, I. Yavneh, R. Basri, Learning to Optimize Multigrid PDE Solvers,
3. J. He, J. Xu, MgNet: a unified framework of multigrid and convolutional neural network, Science china mathematics 62.7 (2019): 1331-1354.
4. R. Huang, R. Li, Y. Xi, Learning optimal multigrid smoothers via neural networks, United States: N. p., 2021. Web.
5. A. Katrutsa T. Daulbaev, Ivan Oseledets, Deep multigrid: learning prolongation and restriction matrices, arxiv 2017.
6. A. Katrutsa T. Daulbaev, Ivan Oseledets, Black-box learning of multigrid parameters, Comput. Appl. Math. 368 (2020) 112524.
7. T. Louw, S. McIntosh-Smith. Applying Recent Machine Learning Approaches to Accelerate the Algebraic Multigrid Method for Fluid Simulations, Smoky Mountains Computational Sciences and Engineering Conference. Springer, Cham, 2021.
8. I. Luz, M. Galun, H. Maron, R. Basri, I. Yavneh, Learning Algebraic Multigrid Using Graph Neural Networks,
9. S. Goswami, A. Bora, Y. Yu, G.E. Karniadakis, Physics-Informed Deep Neural Operator Networks, July 2022.
10. N. Margenberg, R. Jendersie, T. Richter, C. Lessig, Deep neural networks for geometric multigrid methods, June, 2021.
11. P. Suffa Learning Optimal Prolongation and Restriction Operators for Multigrid PDE Solvers, Masterthesis, FAU, 2021.
12. A. Taghibakhshi, S. MacLachlan, L. Olson, M. West, Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning, arxiv, June 2021.
13. S. Wang, H. Wang, P. Perdikaris, Learning the solution operator of parametric partial differential equations with physics-informed DeepONets, Science Advances 7(40) (2021).