Neural-network preconditioners for solving the Dirac equation in lattice gauge theory
This work addresses computational bottlenecks in lattice quantum field theory simulations, offering a scalable approach for physicists, but it is incremental as it builds on existing preconditioning techniques with neural networks.
The paper tackles the problem of accelerating the solution of the Wilson-Dirac normal equation in lattice gauge theory by developing neural-network-based preconditioners, achieving reductions in iterations and operations compared to conventional methods in the two-flavor lattice Schwinger model. It also demonstrates that preconditioners trained on small lattice volumes can be effectively transferred to larger volumes with minimal performance loss.
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.