  For a theoretical understanding of the reactivity of complex chemical
systems, relative energies of stationary points on potential energy
hypersurfaces need to be calculated to high accuracy. Due to the large number
of intermediates present in all but the simplest chemical processes,
approximate quantum chemical methods are required that allow for fast
evaluations of the relative energies, but at the expense of accuracy. Despite
the plethora of benchmark studies, the accuracy of a quantum chemical method is
often difficult to assess. Moreover, a significant improvement of a method's
accuracy (e.g., through reparameterization or systematic model extension) is
rarely possible. Here, we present a new approach that allows for the
systematic, problem-oriented, and rolling improvement of quantum chemical
results through the application of Gaussian processes. Due to its Bayesian
nature, reliable error estimates are provided for each prediction. A reference
method of high accuracy can be employed, if the uncertainty associated with a
particular calculation is above a given threshold. The new data point is then
added to a growing data set in order to continuously improve the model, and as
a result, all subsequent predictions. Previous predictions are validated by the
updated model to ensure that uncertainties remain within the given confidence
bound, which we call backtracking. We demonstrate our approach at the example
of a complex chemical reaction network.

Chemical Physics;Materials Science;Computational Physics;Data Analysis, Statistics and Probability