A local Gaussian Processes method for fitting potential surfaces that obviates the need to invert large matrices

In order to compute a vibrational spectrum, one often wishes start with set of ab initio Born–Oppenheimer potential values at points, called fitting and interpolate or fit find the quadrature collocation points. It is common do this once build energy surface (PES). Once PES known, it can be evaluated any point in configuration space. Gaussian Process (GP) frequently being used make PES. As case other interpolation methods, use GP must store invert matrix whose size number The sometimes large enough that approximations are introduced reduce cost calculation. We show possible many local fits rather than global fit. Retaining only Gaussians associated points works well despite fact have tails significant amplitude region. demonstrate from obtained accurate levels formaldehyde. calculation, were N=120,000 by inverting matrices less m=400. idea reduces N3 T(m3+N), where T desired