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Do you know if there is any work out there on using DL to learn preconditioners to accelerate solution of large scale PDE problems? It looks like there's been a lot of progress with these NN approximations and I think they would be very effective preconditioners
I am not aware of some good examples of this. It is indeed natural to use learning for preconditioning. In a way, our super-resolution models are also learning to precondition
I had been wondering about this since I came across this paper which draws out the relationships between convolutions and geometric multigrid, wish I had more time to dig into it https://arxiv.org/pdf/1901.10415.pdf … Anyway, congrats on a very interesting paper!
Very interesting point @ColinJMcAuliffe. I recently read this article, https://arxiv.org/abs/1906.06925 , thought you might find it interesting. I know of a few groups (including my Ph.D. advisor's) working on this.
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