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We present a new multigrid method called neural multigrid which is based onjoining multigrid ideas with concepts from neural nets. The main idea is to usethe Greenbaum criterion as a cost functional for the neural net. The algorithmis able to learn efficient interpolation operators in the case of the orderedLaplace equation with only a very small critical slowing down and with asurprisingly small amount of work comparable to that of a Conjugate Gradientsolver. In the case of the two-dimensional Laplace equation with SU(2) gaugefields at beta=0 the learning exhibits critical slowing down with an exponentof about z = 0.4. The algorithm is able to find quite good interpolationoperators in this case as well. Thereby it is proven that a practical truemultigrid algorithm exists even for a gauge theory. An improved algorithm usingdynamical blocks that will hopefully overcome the critical slowing downcompletely is sketched.Comment: 13 pages, 3 ps figures, uses IJMPC styl

Another Look at Neural Multigrid