Learning of statistical field theories

We show that statistical field theories can be rigorously learned from measured expectations of physical observables or from data obtained in first-principles simulations. This holds true even for strongly interacting theories. To this end, we develop and test a family of estimators for the parameters of discrete and continuous lattice gauge theories based on the Interaction Screening and Score Matching methods. We study the sample complexities of these estimators on high-dimensional models that include discrete Wegner's Ising lattice gauge theory, scalar field theories, Schwinger model, and sine-Gordon theory. As an application of our learning-based method, we investigate RG effects like the running of coupling constants. We anticipate that our approach will provide an avenue towards efficient non-perturbative methods and will contribute to automating the discovery of effective field theories across different scales.