  We present novel non-parametric representation math for local
pseudopotentials (PP) based on Gaussian Process Regression (GPR). Local
pseudopotentials are needed for materials simulations using Orbital-Free
Density Functional Theory (OF-DFT) to reduce computational cost and to allow
kinetic energy functional (KEF) application only to the valence density.
Moreover, local PPs are important for the development of accurate KEFs for
OF-DFT as they are only available for a limited number of elements. We optimize
local PPs of tin (Sn) using GP regression to reproduce the experimental lattice
constants of {\alpha}- and \b{eta}-Sn, the energy difference between these two
phases as well as their electronic structure and charge density distributions,
which are obtained with Kohn-Sham Density Functional Theory employing
semi-local PPs. The use of a non-parametric GPR-based PP representation avoids
difficulties associated with the use of parametrized functions and has the
potential to construct an optimal local PP independent of prior assumptions.
The GPR-based Sn local PP results in well-reproduced bulk properties of
{\alpha}- and \b{eta}-tin, and electronic valence densities similar to those
obtained with semi-local PP.
