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We present novel non-parametric representation math for localpseudopotentials (PP) based on Gaussian Process Regression (GPR). Localpseudopotentials are needed for materials simulations using Orbital-FreeDensity Functional Theory (OF-DFT) to reduce computational cost and to allowkinetic energy functional (KEF) application only to the valence density.Moreover, local PPs are important for the development of accurate KEFs forOF-DFT as they are only available for a limited number of elements. We optimizelocal PPs of tin (Sn) using GP regression to reproduce the experimental latticeconstants of {\alpha}- and \b{eta}-Sn, the energy difference between these twophases as well as their electronic structure and charge density distributions,which are obtained with Kohn-Sham Density Functional Theory employingsemi-local PPs. The use of a non-parametric GPR-based PP representation avoidsdifficulties associated with the use of parametrized functions and has thepotential 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 thoseobtained with semi-local PP.

Non-parametric Local Pseudopotentials with Machine Learning: a Tin Pseudopotential Built Using Gaussian Process Regression