The paper is organized as follows. We first set the stage in Sec. II A by elaborating on the LES and GES for ML DFAs. Then, in Sec. II B we introduce our proxy reference energy densities, that we use to contrast the extrapolation power of LES and GES in Sec. III. Finally, a real-space, ML-based and regularized SCS PT2 model for correlation energy densities is presented in Sec. IV.