Parameter optimization in differential geometry based solvation models

TL;DR

This paper introduces new parameter optimization algorithms for differential geometry based solvation models, significantly improving their stability and accuracy in predicting solvation free energies for diverse molecules.

Contribution

It presents novel perturbation and convex optimization methods to stabilize and optimally parametrize DG-based solvation models, enabling unified and accurate solvation energy predictions.

Findings

Achieves highly accurate solvation free energy predictions.

Demonstrates stability and robustness of the new parametrization.

Outperforms existing methods in predictive accuracy.

Abstract

Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and nonpolar interactions in a self-consistent framework. Our earlier study indicates that DG based nonpolar solvation model outperforms other methods in nonpolar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and nonploar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.