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We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows for lattice field theory, we propose the ``partitioning flow-based Markov chain Monte Carlo (PFMCMC) sampling" method to address two challenges encountered in normalizing flow applications for lattice field theory: the ``mode-collapse" and ``rare-event sampling" problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the effectiveness of our PFMCMC method in modeling highly hierarchical order parameter probability distributions and simulating critical bubble configurations. These simulations are then used to facilitate the calculation of nucleation rates. We anticipate the application of this method to (3+1)-dimensional theories for studying realistic cosmological phase transitions.
Bai et al. (Sun,) studied this question.