  The combination of transfer learning (TL) a low level potential energy
surface (PES) to a higher level of electronic structure theory together with
ring-polymer instanton (RPI) theory is explored and applied to malonaldehyde.
The RPI approach provides a semiclassical approximation of the tunneling
splitting and depends sensitively on the accuracy of the PES. With second order
M{\o}ller-Plesset perturbation theory (MP2) as the low-level (LL) model and
energies and forces from coupled cluster singles, doubles and perturbative
triples (CCSD(T)) as the high-level (HL) model, it is demonstrated that CCSD(T)
information from only 25 to 50 judiciously selected structures along and around
the instanton path suffice to reach HL-accuracy for the tunneling splitting. In
addition, the global quality of the HL-PES is demonstrated through a mean
average error of 0.3 kcal/mol for energies up to 40 kcal/mol above the minimum
energy structure (a factor of 2 higher than the energies employed during TL)
and $< 2 $ cm$^{-1}$ for harmonic frequencies compared with computationally
challenging normal mode calculations at the CCSD(T) level.
