Training set design for machine learning techniques applied to the approximation of computationally intensive first-principles kinetic models

We propose a design procedure for the generation of the training set for Machine Learning algorithms with a specific focus on the approximation of computationally-intensive first-principles kinetic models in catalysis. The procedure is based on the function topology and behavior, by means of the calculation of the discrete gradient, and on the relative importance of the independent variables. We apply the proposed methodology to the tabulation and regression of mean-field and kinetic Monte Carlo models aiming at their coupling with reactor simulations. Our tests - in the context both of mean-field kinetics and kinetic Monte Carlo simulations - show that the procedure is able to design a dataset that requires between 60 and 80% fewer data points to achieve the same approximation accuracy than the one obtained with an evenly distributed grid. This strong reduction in the number of points results in a significant computational gain and a concomitant boost of the approximation efficiency. The Machine Learning algorithms trained with the results of the procedure are then included in both macroscopic reactor models and computational fluid dynamics (CFD) simulations. First, a Plug Flow Reactor is employed to carry out a direct comparison with the solution of the full first-principles kinetic model. The results show an excellent agreement within 0.2% between the models. Then, the CFD simulation of complex tridimensional geometry is carried out by using a tabulated kMC model for CO oxidation on Ruthenium oxide, thus providing a showcase of the capability of the approach in making possible the multiscale simulation of complex chemical reactors.