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

• URL: http://arxiv.org/abs/2208.02728v1
• Date: Thu, 4 Aug 2022 15:50:41 GMT
• Title: Neural-network preconditioners for solving the Dirac equation in lattice gauge theory
• Authors: Salvatore Cal\`i, Daniel C. Hackett, Yin Lin, Phiala E. Shanahan, Brian Xiao
• Abstract summary: This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. 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.
• Score: 0.5999777817331318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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