Stochastic approximation Monte Carlo with a dynamic update factor

Abstract

We present a new Monte-Carlo algorithm based on the Stochastic Approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is Stochastic Approximation with a Dynamic update factor (SAD) which dynamically adjusts the update factor γ during the course of the simulation. We test this method on the square-well fluid and compare the convergence time and average entropy error for several related Monte-Carlo methods. We find that both the SAD and 1/t-Wang-Landau (1/t-WL) methods rapidly converge to the correct density of states without the need for the user to specify an arbitrary tunable parameter t0 as in the case of SAMC. SAD requires as input the temperature range of interst, in contrast to 1/t-WL, which requires that the user identify the interesting range of energies. Thus SAD is more convenient when the range of energies is not known in advance.

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“…Pommerenck et al propose a refinement [21] to SAMC where the update factor is determined dynamically rather than by the user. Stochastic Approximation with a dynamic γ (SAD) requires the user to provide the lowest temperature of interest T min .…”

“…The SAD (Stochastic Approximation with Dynamic γ) method outlined by Pommerenck et.al [21] is a special version of the SAMC algorithm that dynamically chooses the modification factor rather than relying on system dependent parameters. SAD shares the same convergence properties with SAMC while replacing un-physical userdefined parameters with the algorithms dynamic choice.…”