Neural-network preconditioners for solving the Dirac equation in lattice gauge theory

Abstract

This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical point. In this system, neural-network preconditioners are found to accelerate the convergence of the conjugate gradient solver compared with the solution of unpreconditioned systems or those preconditioned with conventional approaches based on even-odd or incomplete Cholesky decompositions, as measured by reductions in the number of iterations and/or complex operations required for convergence. It is also shown that a preconditioner trained on ensembles with small lattice volumes can be used to construct preconditioners for ensembles with many times larger lattice volumes, with minimal degradation of performance. This volume-transferring technique amortizes the training cost and presents a pathway towards scaling such preconditioners to lattice field theory calculations with larger lattice volumes and in four dimensions.

11 pages, 6 figures, and 2 tables

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Cited by in corpus (3)

• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Gauge covariant neural network for quarks and gluons
• Applications of flow models to the generation of correlated lattice QCD ensembles