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In this paper we propose new algorithm to reduce autocorrelation in Markovchain Monte-Carlo algorithms for euclidean field theories on the lattice. Ourproposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restrictedBoltzmann machine. We examine the validity of the algorithm by employing thephi-fourth theory in three dimension. We observe reduction of theautocorrelation both in symmetric and broken phase as well. Our proposingalgorithm provides consistent central values of expectation values of theaction density and one-point Green's function with ones from the original HMCin both the symmetric phase and broken phase within the statistical error. Onthe other hand, two-point Green's functions have slight difference between onecalculated by the HMC and one by our proposing algorithm in the symmetricphase. Furthermore, near the criticality, the distribution of the one-pointGreen's function differs from the one from HMC. We discuss the origin ofdiscrepancies and its improvement.

Towards reduction of autocorrelation in HMC by machine learning