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Efficient Learning of Lattice Gauge Theories with Fermions
Shreya Shukla, Yukari Yamauchi, Andrey Y. Lokhov, Scott Lawrence, Abhijith Jayakumar·December 22, 2025
hep-latcs.LGQuantum Physics
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Abstract
We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.