  Monte Carlo (MC) methods are important computational tools for molecular
structure optimizations and predictions. When solvent effects are explicitly
considered, MC methods become very expensive due to the large degree of freedom
associated with the water molecules and mobile ions. Alternatively
implicit-solvent MC can largely reduce the computational cost by applying a
mean field approximation to solvent effects and meanwhile maintains the atomic
detail of the target molecule. The two most popular implicit-solvent models are
the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way
such that the GB model is an approximation to the PB model but is much faster
in simulation time. In this work, we develop a machine learning-based
implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both
implicit solvent models in accuracy and efficiency. Specifically, the MLIMC
method uses a fast and accurate PB-based machine learning (PBML) scheme to
compute the electrostatic solvation free energy at each step. We validate our
MLIMC method by using a benzene-water system and a protein-water system. We
show that the proposed MLIMC method has great advantages in speed and accuracy
for molecular structure optimization and prediction.
