Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for Multivariate Function Representation: Application to Molecular Potential Energy Surfaces

We
present an approach combining a representation of a multivariate
function using subdimensional functions with machine learning based
representation of component functions: Random sampling high dimensional
model representation Gaussian process regression (RS-HDMR-GPR). The
use of Gaussian process regressions to represent component functions
allows nonparametric (unbiased) representation and the possibility
to work only with functions of desired dimensionality, obviating the
need to build an expansion over orders of coupling. All component
functions are determined from a single set of samples. The method
is tested by fitting six- and 15-dimensional potential energy surfaces
(PES) of polyatomic molecules as well as by computing vibrational
spectra for a four-atomic molecule.