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.

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

“…Therefore, most pairs of (M, M s ) considered can finish the simulation within a few minutes to a few hours. However, some edge windows may get 'stuck' at energy levels with low DOS [37,56,57] and do not converge after several days, especially when the sampling points include M s = 0. Therefore, we reject a simulation that does not finish in two days and re-start the run.…”

“…11). That means that if we we can get a perfect result with a small system size L s , when we consider a bigger system L b , the increment has to be chosen such that As the number of (M, M s ) pairs that must be sampled is L 4 /M 2 const , the minimum number The occurrence of 'stuck' simulation runs has also been observed in other WL based algorithms [37,56,57], particularly in phase regions of extreme energy and/or very low DOS. It is thus not a specific consequence of the macroscopic constraints in the present method.…”

Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang–Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics

“…A more recent development in the metadynamics community concerns adaptive Gaussians [25], where the form of the update to the bias potential depends on local properties of the underlying free-energy surface. Similar ideas of applying different entropy updates in Wang-Landau simulations have circulated [26] and an ad-hoc method for nonuniform binning of energy levels has been recently and independently implemented [27]. To mention a final example, in efforts to develop massively parallel implementations, multiple parallel walkers have been simultaneously deployed to update a bias potential in metadynamics [28].…”

Stochastic approximation Monte Carlo with a dynamic update factor

“…Energy bins are typically of uniform size for the entire energy continuum [23]. Some methods such as AdaWL [24] employ a tunable mechanism for controlling the binning for low entropic states in order to ensure the exploration of all energies. The method introduced in this paper is designed to scale appropriately as bin size is changed, but we do not test this scaling, as we use a system with discrete energy levels.…”