ct0c00257_si_002.zip (1.2 MB)
Restricted-Variance Molecular Geometry Optimization Based on Gradient-Enhanced Kriging
dataset
posted on 2020-05-19, 20:29 authored by Gerardo Raggi, Ignacio Fdez. Galván, Christian L. Ritterhoff, Morgane Vacher, Roland LindhMachine learning techniques, specifically
gradient-enhanced Kriging
(GEK), have been implemented for molecular geometry optimization.
GEK-based optimization has many advantages compared to conventionalstep-restricted
second-order truncated expansionmolecular optimization methods.
In particular, the surrogate model given by GEK can have multiple
stationary points, will smoothly converge to the exact model as the
number of sample points increases, and contains an explicit expression
for the expected error of the model function at an arbitrary point.
Machine learning is, however, associated with abundance of data, contrary
to the situation desired for efficient geometry optimizations. In
this paper, we demonstrate how the GEK procedure can be utilized in
a fashion such that in the presence of few data points, the surrogate
surface will in a robust way guide the optimization to a minimum of
a potential energy surface. In this respect, the GEK procedure will
be used to mimic the behavior of a conventional second-order scheme
but retaining the flexibility of the superior machine learning approach.
Moreover, the expected error will be used in the optimizations to
facilitate restricted-variance optimizations. A procedure which relates
the eigenvalues of the approximate guessed Hessian with the individual
characteristic lengths, used in the GEK model, reduces the number
of empirical parameters to optimize to two: the value of the trend
function and the maximum allowed variance. These parameters are determined
using the extended Baker (e-Baker) and part of the Baker transition-state
(Baker-TS) test suites as a training set. The so-created optimization
procedure is tested using the e-Baker, full Baker-TS, and S22 test
suites, at the density functional theory and second-order Møller–Plesset
levels of approximation. The results show that the new method is generally
of similar or better performance than a state-of-the-art conventional
method, even for cases where no significant improvement was expected.