Sampling U(1) gauge theory using a re-trainable conditional flow-based model

Sampling topological quantities in the Monte Carlo simulation of Lattice Gauge Theory becomes challenging as we approach the continuum limit of the theory. In this work, we introduce a Conditional Normalizing Flow (C-NF) model to sample U(1) gauge theory in two dimensions, aiming to mitigate the impact of topological freezing when dealing with smaller values of the U(1) bare coupling. To train the conditional flow model, we utilize samples generated by Hybrid Monte Carlo (HMC) method, ensuring that the autocorrelation in topological quantities remains low. Subsequently, we employ the trained model to interpolate the coupling parameter to values where training was not performed. We thoroughly examine the quality of the model in this region and generate uncorrelated samples, significantly reducing the occurrence of topological freezing. Furthermore, we propose a re-trainable approach that utilizes the model's own samples to enhance the generalization capability of the conditional model. This method enables sampling for coupling values that are far beyond the initial training region, expanding the applicability of the model.