A Multifidelity Monte Carlo Approach for Simulating the Diffusion Coefficient of Water. I. Forward Problem

A multi-fidelity Monte Carlo framework for molecular dynamics simulations of the diffusion coefficient of liquid water is presented. The model hierarchy is constructed based on the size of the simulation box, taking advantage of the well-known size effects that simulations of the diffusion coefficient suffer from. Water is represented as a rigid three-point model, and uncertainties in the non-bonded force field parameters i.e., the Lennard-Jones parameters and partial charges, are propagated forward through the simulations. A large-scale study exploring the capabilities of the multifidelity Monte Carlo framework is conducted, involving six computational models, three different calibrations, cubic and tetragonal simulation box shapes, and two sets of perturbed force field parameters. Results reveal that significant computational speed-ups of up to one order of magnitude can be achieved if successive models have small differences in correlations to the high-fidelity model. It is also found that the combination of high- and low-fidelity models provides a computational speed-up compared to exclusively relying on a single high-fidelity model in almost all cases.