Smart random walks for accelerated Monte Carlo simulations

Monte Carlo simulations are robust methods to study statistical physics. However, the unpredictable convergence time and the ease of being trapped in local minima have plagued the efficiency of both traditional and modern Monte Carlo algorithms. We propose strategies to mitigate these problems. We highlight two recent algorithmic developments: the histogram-free multicanonical method for obtaining the density of states for physical systems [1], and a global update scheme that adjusts the sampling weights across the phase space simultaneously. Combining these two methods, we have observed speedups ranging from 1-3 orders of magnitude compared to existing flat-histogram methods such as Wang-Landau sampling and multicanonical sampling, depending on the problem of interest. These methods are implemented and publicly available in an open-source Monte Carlo software suite, the Oak-ridge/Open-source Wang-Landau (OWL) code [2].

[1] A. C. K. Farris, Y. W. Li and M. Eisenbach, Comput. Phys. Comm. 235, 297-394 (2019).
[2] GitHub repository of OWL: https://github.com/owl-suite/OWL .