Towards reduction of autocorrelation in HMC by machine learning
This work addresses autocorrelation issues in MCMC simulations for physicists, but it is incremental as it builds on existing HMC methods with a machine learning component.
The authors tackled the problem of autocorrelation in Hybrid Monte-Carlo algorithms for lattice field theories by integrating a restricted Boltzmann machine, observing reduced autocorrelation in both symmetric and broken phases of a 3D phi-fourth theory.
In this paper we propose new algorithm to reduce autocorrelation in Markov chain Monte-Carlo algorithms for euclidean field theories on the lattice. Our proposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted Boltzmann machine. We examine the validity of the algorithm by employing the phi-fourth theory in three dimension. We observe reduction of the autocorrelation both in symmetric and broken phase as well. Our proposing algorithm provides consistent central values of expectation values of the action density and one-point Green's function with ones from the original HMC in both the symmetric phase and broken phase within the statistical error. On the other hand, two-point Green's functions have slight difference between one calculated by the HMC and one by our proposing algorithm in the symmetric phase. Furthermore, near the criticality, the distribution of the one-point Green's function differs from the one from HMC. We discuss the origin of discrepancies and its improvement.