Fast Adaptive Flat-histogram Ensemble for Calculating Density of States and Enhanced Sampling in Large Systems

TL;DR

The paper introduces FAFE, an efficient algorithm for estimating the density of states and enhancing sampling in large systems, outperforming previous methods in speed and accuracy.

Contribution

FAFE is a novel algorithm that satisfies detailed balance and automatically adapts data points, significantly reducing simulation steps for large systems.

Findings

FAFE reduces simulation steps from O(N^{3/2}) to O(N^{1/2})

Demonstrated efficiency in Lennard-Jones liquids with various sizes

Able to identify different macroscopic states and metastable states

Abstract

We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable $U$ in generalized ensembles to form points on the curve $\beta_{s}(U) \equiv \frac{\partial S(U)}{\partial U}$, the derivative of the logarithmic DOS. Unlike the popular Wang-Landau-like (WLL) methods, FAFE satisfies the detailed-balance condition through out the simulation and automatically generates non-uniform $(\beta_{i}, U_{i})$ data points to follow the real change rate of $\beta_{s}(U)$ in different $U$ regions and in different systems. Combined with a $U-$compression transformation, FAFE reduces the required simulation steps from $O(N^{3/2})$ in WLL to $O(N^{1/2})$, where $N$ is the system size. We demonstrate the efficiency of FAFE in Lennard-Jones liquids with several $N$ values. More importantly, we show its abilities in finding and identifying different macroscopic states including meta-stable states in phase co-existing regions.