A 1/t algorithm with the density of two states for estimating multidimensional integrals

Atisattapong, Wanyok; Marupanthorn, Pasin

doi:10.1016/j.cpc.2017.06.024

Cited by 3 publications

(1 citation statement)

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“…Assume that WL has been run, and denote y i the average value of function f computed over all points such that f (x) ∈ [y i , y i + dy]. The integral can be estimated as [21] I ≈ i=1,...,n θ N orm…”

Section: Numerical Integrationmentioning

confidence: 99%

Wang-Landau algorithm: An adapted random walk to boost convergence

Chevallier¹,

Cazals²

2020

Journal of Computational Physics

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The Wang-Landau (WL) algorithm is a recently developed stochastic algorithm computing densities of states of a physical system. Since its inception, it has been used on a variety of (bio-)physical systems, and in selected cases, its convergence has been proved. The convergence speed of the algorithm is tightly tied to the connectivity properties of the underlying random walk. As such, we propose an efficient random walk that uses geometrical information to circumvent the following inherent difficulties: avoiding overstepping strata, toning down concentration phenomena in high-dimensional spaces, and accommodating multidimensional distribution. Experiments on various models stress the importance of these improvements to make WL effective in challenging cases. Altogether, these improvements make it possible to compute density of states for regions of the phase space of small biomolecules.

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Section: Numerical Integrationmentioning

confidence: 99%