Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes

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 with the example of a complex chemical reaction network.