Multigrid meets Neural Nets

TL;DR

This paper demonstrates the effectiveness of multigrid methods for wave equations in disordered systems and introduces a neural computation perspective to improve large-scale simulations, enabling faster and more efficient computations.

Contribution

It combines multigrid techniques with neural network insights to enhance simulation efficiency and introduces neural-based interpolation kernels for multigrid Monte Carlo methods.

Findings

Multigrid effectively solves wave equations in disordered systems.

Neural computations can optimize large-scale simulation processes.

Neural interpolation kernels improve multigrid Monte Carlo updates.

Abstract

We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We 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.