Efficient Learning of Lattice Gauge Theories with Fermions
This enables more efficient parameter estimation in lattice gauge theories, which is crucial for physicists studying quantum field theories, though it appears incremental as an extension of existing score matching methods.
The authors tackled the problem of recovering action parameters in lattice field theories by introducing a learning method based on minimizing a convex loss function derived from Schwinger-Dyson relations, extending it to realistic theories like quantum chromodynamics with fermions.
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.