Potential-Decomposition Strategy in Markov Chain Monte Carlo Sampling Algorithms

We introduce the potential-decomposition strategy (PDS), which can be used in Markov chain Monte Carlosampling algorithms.PDS can be designed to make particles move in a modified potential that favors diffusion in phasespace, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner.Furthermore,if the accepted trial samples are insufficient, they can be recycled as initial states to form more unbiased samples.Thisstrategy can greatly improve efficiency when the original potential has multiple metastable states separated by largebarriers.We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating inthese two representative examples that convergence is accelerated by orders of magnitude.

We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.