Machine learning based surrogate models that interpolate precomputed solutions of the rate equations can greatly accelerate simulations of catalytic systems. Established schemes for the construction of surrogate models depend on a logarithmic scaling of the source terms, which limits their application to cases where species are exclusively consumed or produced under all conditions of interest. We propose a new approach based on interpolating the forward- and reverse rates of the rate-determining reactions and thus overcoming this limitation. The new scheme is demonstrated using a surface reaction mechanism describing the oxidation of CO and H2 as well as the water gas shift reaction including 5 gas species, 9 surface species and 18 reversible reactions. Multivariate spline interpolation is used for a first evaluation of our approach. With the splines, the new method reproduces the source terms of CO with an error of 0.5 % which is 50 to 100 times more accurate than the established approaches of either mapping the source terms directly (49.9 % error) or mapping adsorption/desorption rates (23.7 % error). The true potential of the new approach develops in combination with machine learning techniques like neural networks. Even very small neural networks with a single hidden layer of 20 nodes yield an error of 0.35 %. This is about 200 times more accurate than the same neural networks used with the established approaches. Increasing the network size to still moderate 30 nodes in two hidden layers (2342 parameters in total) reduces the error to 0.0058 %. Besides the increased accuracy, the neural networks also outperform spline interpolation by at least an order of magnitude with respect to interpolation time, storage space and required amount of training data. Due to the extremely low errors achieved with moderate size neural networks and small training data sets, the proposed method based on mapping the rate-determining steps shows promise to scale to much larger and more complex reaction systems in catalysis and other fields like combustion, atmospheric chemistry or systems biology.