Speaker
Description
The low-lying modes of the Wilson Dirac operator are key ingredients in deflation and multigrid algorithms for lattice QCD, where they define the near-null spaces responsible for critical slowing down. In this talk, we present a method for learning such low modes with a gauge-equivariant neural network trained on an ensemble of gauge configurations, using a Rayleigh–Ritz loss that minimizes the sum of the lowest Rayleigh quotients of $D^\dagger D$. Because the network is trained across the ensemble rather than per configuration, its setup cost can be amortized over many solves. We report the generalization of the learned modes to held-out configurations on small lattices, and demonstrate their effectiveness as test vectors in the DD-$\alpha$AMG multigrid solver.