Another Look at Neural Multigrid

Martin Bäker ()
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Martin Bäker: Institut für Werkstoffe, Technische Universität Braunschweig, Langer Kamp 8, 38106 Braunschweig, Germany

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 02, 191-205

Abstract: 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 solverIn the case of the two-dimensional Laplace equation with SU(2) gauge fields at β = 0 the learning exhibits critical slowing down with an exponent of aboutz≈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.

Keywords: Discretized Differential Equations; Multigrid; Neural Nets; Disordered Systems; Lattice Gauge Theory (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S0129183197000187

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