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Gauge-equivariant neural networks as preconditioners in lattice QCD
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We demonstrate that a state-of-the art multi-grid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal re-training on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.
Forward citations
Cited by 3 Pith papers
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Neural network interpolators for Wilson loops
Neural networks parametrize gauge-equivariant trial states for Wilson loops and automatically yield interpolators for ground and excited states in quenched lattice QCD.
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Wilson loops with neural networks
Neural networks parametrize gauge-invariant interpolators that extract ground-state Wilson loops with improved signal-to-noise ratio compared to traditional methods while preserving gauge invariance.
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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory
A matrix-free neural preconditioner learns to map gauge configurations to modified configurations whose Dirac operators approximate the inverse, halving CG iterations and transferring across lattice sizes.
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