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The combination of transfer learning (TL) a low level potential energysurface (PES) to a higher level of electronic structure theory together withring-polymer instanton (RPI) theory is explored and applied to malonaldehyde.The RPI approach provides a semiclassical approximation of the tunnelingsplitting and depends sensitively on the accuracy of the PES. With second orderM{\o}ller-Plesset perturbation theory (MP2) as the low-level (LL) model andenergies and forces from coupled cluster singles, doubles and perturbativetriples (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 aroundthe instanton path suffice to reach HL-accuracy for the tunneling splitting. Inaddition, the global quality of the HL-PES is demonstrated through a meanaverage error of 0.3 kcal/mol for energies up to 40 kcal/mol above the minimumenergy structure (a factor of 2 higher than the energies employed during TL)and $< 2 $ cm$^{-1}$ for harmonic frequencies compared with computationallychallenging normal mode calculations at the CCSD(T) level.

Transfer learning for affordable and high quality tunneling splittings from instanton calculations