Neural-network approaches for preconditioning the Dirac equation in lattice QCD

by Simon Pfahler (University of Regensburg)

Tuesday 26 May 2026, 15:00 → 17:00 Europe/Berlin

Nußallee 14-16/0.023 (HISKP) - Lecture Hall (HISKP)

Lattice QCD simulations are computationally expensive, with the solution of the Dirac equation being the major computational bottleneck of many calculations. Preconditioners can drastically reduce this computational cost. We introduce a gauge-equivariant neural-network architecture for preconditioning the Dirac equation in the regime where critical slowing down occurs, without needing fine-tuning to a specific gauge configuration. By comparing the learned model weights to the analytical structure of existing methods, we can not only compare runtime of test solves, but can get an idea of what the models can and can not learn.