Neural multigrid for gauge theories and other disordered systems

TL;DR

This paper demonstrates that neural multigrid methods can efficiently solve wave equations in highly disordered gauge systems, emphasizing the importance of learning-based approaches for large-scale simulations and interpolation in Monte Carlo methods.

Contribution

It introduces a neural multigrid approach that adapts to disordered gauge systems, enabling efficient simulations and improved interpolation kernels.

Findings

Neural multigrid effectively solves wave equations with strong disorder.

The method enhances multigrid Monte Carlo updates.

Learning is essential for efficiency in large-scale disordered systems.

Abstract

We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.