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Sampling topological quantities in the Monte Carlo simulation of LatticeGauge Theory becomes challenging as we approach the continuum limit of thetheory. In this work, we introduce a Conditional Normalizing Flow (C-NF) modelto sample U(1) gauge theory in two dimensions, aiming to mitigate the impact oftopological freezing when dealing with smaller values of the U(1) barecoupling. To train the conditional flow model, we utilize samples generated byHybrid Monte Carlo (HMC) method, ensuring that the autocorrelation intopological quantities remains low. Subsequently, we employ the trained modelto interpolate the coupling parameter to values where training was notperformed. We thoroughly examine the quality of the model in this region andgenerate uncorrelated samples, significantly reducing the occurrence oftopological freezing. Furthermore, we propose a re-trainable approach thatutilizes the model's own samples to enhance the generalization capability ofthe conditional model. This method enables sampling for coupling values thatare far beyond the initial training region, expanding the applicability of themodel.

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