Sharp Restart in Walk-on-Subdomains

Monte Carlo methods are often used to efficiently estimate partial differential equations. In this document, I will look at a few methods that have been developed into the backbone of the algorithm for estimating the electrostatic free energy of a biomolecule in a solution. Then, I will examine a problem found in the Walk-on-Subdomains (WOSD) portion of this algorithm. In some cases, walkers get stuck oscillating between two atoms, which can cause the run to take an incredibly long time to complete. I will also present a potential solution to this problem, using a sharp restart condition. Using some ideas from research into First Passage Time (FPT) algorithms, this method could both solve the problem of walker entrapment and perhaps improve overall run time even when significant entrapment has not occurred. I will examine some experimental results for both improved run time and potential bias in the final results. Finally, I test two automated methods for determining an appropriate sharp restart condition and evaluate whether automating the restart appears appropriate for use in arbitrary molecules.