A statistically guided grid generation method and its application to intermolecular potential energy surfaces

Abstract

We present a method for the generation of points in space needed to create training data for fitting of nonlinear parametric models. This method uses statistical information extracted from an initial fit on a sparse grid to select optimal grid points in an iterative manner and is, therefore, called the iterative variance minimizing grid approach. We demonstrate the method in the case of six-dimensional intermolecular potential energy surfaces (PESs) fitted to ab initio computed interaction energies. The number of required grid points is reduced by roughly a factor of two in comparison to alternative systematic sampling methods. The method is not limited to fitting PESs and can be applied to any cases of fitting parametric models where data points may be chosen freely but are expensive to obtain.