Another Look at Neural Multigrid

Details Another Look at Neural Multigrid Another Look at Neural Multigrid

1996-10-25

arxiv.org/abs/hep-lat/9610035v1

Int.J.Mod.Phys. C8 (1997) 191-205

Physics

High Energy Physics

High Energy Physics - Lattice

13 pages, 3 ps figures, uses IJMPC style

Scientific paper

We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is able to learn efficient interpolation operators in the case of the ordered Laplace equation with only a very small critical slowing down and with a surprisingly small amount of work comparable to that of a Conjugate Gradient solver. In the case of the two-dimensional Laplace equation with SU(2) gauge fields at beta=0 the learning exhibits critical slowing down with an exponent of about z = 0.4. The algorithm is able to find quite good interpolation operators in this case as well. Thereby it is proven that a practical true multigrid algorithm exists even for a gauge theory. An improved algorithm using dynamical blocks that will hopefully overcome the critical slowing down completely is sketched.

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