Dynamically Optimized Wang-Landau Sampling with Adaptive Trial Moves and Modification Factors

Abstract

The density of states of continuous models is known to span many orders of magnitudes at different energies due to the small volume of phase space near the ground state. Consequently, the traditional Wang-Landau sampling which uses the same trial move for all energies faces difficulties sampling the low entropic states. We developed an adaptive variant of the Wang-Landau algorithm that very effectively samples the density of states of continuous models across the entire energy range. By extending the acceptance ratio method of Bouzida, Kumar, and Swendsen such that the step size of the trial move and acceptance rate are adapted in an energy-dependent fashion, the random walker efficiently adapts its sampling according to the local phase space structure. The Wang-Landau modification factor is also made energy-dependent in accordance with the step size, enhancing the accumulation of the density of states. Numerical simulations show that our proposed method performs much better than the traditional Wang-Landau sampling.

Accepted for Physical Review E

References in corpus (4)

• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Optimal Modification Factor and Convergence of the Wang-Landau Algorithm
• Improving Wang-Landau sampling with adaptive windows
• Wang-Landau study of the 3D Ising model with bond disorder

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• Complex free energy landscapes in biaxial nematics and role of repulsive interactions : A Wang - Landau study
• Efficient sampling using Macrocanonical Monte Carlo and density of states mapping
• Stochastic Approximation Monte Carlo with a Dynamic Update Factor