  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.
