  The interpolation of high-dimensional potential energy surfaces (PESs) is
commonly done with physically-inspired deep-neural network models. In this
work, we illustrate that Gaussian Processes (GPs) are also capable of
interpolating high-dimensional complex physical systems. The accuracy of GPs
depends on the robustness of the kernel function, and a boost in the accuracy
is achieved by linearly combining kernel functions. In this work, we proposed
an alternative route by parametrizing the kernel function through Bochners'
theorem. We interpolated the PES of various chemical systems achieving a global
accuracy of < 0.06 kcal/mol for Benzene, Malonaldehyde, Ethanol, and protonated
Imidazole dimer using only 15 000 training points. Additionally, for Aspirin,
we achieved a global error of 0.063 kcal/mol with 20 000 points. Given these
results, we believe this kernel function is system-agnostic and could allow GPs
to tackle a wider variety of high-dimensional physical systems.
