  Accurate ab-initio prediction of electronic energies is very expensive for
macromolecules by explicitly solving post-Hartree-Fock equations. We here
exploit the physically justified local correlation feature in compact basis of
small molecules, and construct an expressive low-data deep neural network (dNN)
model to obtain machine-learned electron correlation energies on par with MP2
and CCSD levels of theory for more complex molecules and different datasets
that are not represented in the training set. We show that our dNN-powered
model is data efficient and makes highly transferable prediction across alkanes
of various lengths, organic molecules with non-covalent and biomolecular
interactions, as well as water clusters of different sizes and morphologies. In
particular, by training 800 (H$_2$O)$_8$ clusters with the local correlation
descriptors, accurate MP2/cc-pVTZ correlation energies up to (H$_2$O)$_{128}$
can be predicted with a small random error within chemical accuracy from exact
values, while a majority of prediction deviations are attributed to an
intrinsically systematic error. Our results reveal that an extremely compact
local correlation feature set, which is poor for any direct post-Hartree-Fock
calculations, has however a prominent advantage in reserving important electron
correlation patterns for making accurate transferable predictions across
distinct molecular compositions, bond types and geometries.
