Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations
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We provide a deepened study of autocorrelations in Neural Markov Chain Monte Carlo simulations, a version of the traditional Metropolis algorithm which employs neural networks to provide independent proposals. We illustrate our ideas using the two-dimensional Ising model. We propose several estimates of autocorrelation times, some inspired by analytical results derived for the Metropolized Independent Sampler, which we compare and study as a function of inverse temperature β. Based on that we propose an alternative loss function and study its impact on the autocorelation times. Furthermore, we investigate the impact of imposing system symmetries (Z_2 and/or translational) in the neural network training process on the autocorrelation times. Eventually, we propose a scheme which incorporates partial heat-bath updates. The impact of the above enhancements is discussed for a 16 × 16 spin system. The summary of our findings may serve as a guide to the implementation of Neural Markov Chain Monte Carlo simulations of more complicated models.
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