  Ab initio instanton rate theory is a computational method for rigorously
including tunnelling effects into calculations of chemical reaction rates based
on a potential-energy surface computed on the fly from electronic-structure
theory. This approach is necessary to extend conventional transition-state
theory into the deep-tunnelling regime, but is also more computationally
expensive as it requires many more ab initio calculations. We propose an
approach which uses Gaussian process regression to fit the potential-energy
surface locally around the dominant tunnelling pathway. The method can be
converged to give the same result as from an on-the-fly ab initio instanton
calculation but requires far fewer electronic-structure calculations. This
makes it a practical approach for obtaining accurate rate constants based on
high-level electronic-structure methods. We show fast convergence to reproduce
benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in
full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.
