The conversion of $\mathrm{CO_2}$ into useful products such as methanol is a key strategy for abating climate change and our dependence on fossil fuels. Developing new catalysts for this process is costly and time-consuming and can thus benefit from computational exploration of possible active sites. However, this is complicated by the complexity of the materials and reaction networks. Here, we present a workflow for exploring transition states of elementary reaction steps at inverse catalysts, which is based on the training of a neural network-based machine learning interatomic potential. We focus on the crucial formate intermediate and its formation over nanoclusters of indium oxide supported on Cu(111). The speedup compared to an approach purely based on density functional theory allows us to probe a wide variety of active sites found at nanoclusters of different sizes and stoichiometries. Analysis of the obtained set of transition state geometries reveals different structure--activity trends at the edge or interior of the nanoclusters. Furthermore, the identified geometries allow for the breaking of linear scaling relations, which could be a key underlying reason for the excellent catalytic performance of inverse catalysts observed in experiments.

Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a machine learning method for constructing high-dimensional potential energy surfaces based on feed-forward neural networks. As input to the neural network we propose an extendable invariant local molecular descriptor constructed from geometric moments. Their formulation via pairwise distance vectors and tensor contractions allows a very efficient implementation on graphical processing units (GPUs). The atomic species is encoded in the molecular descriptor, which allows the restriction to one neural network for the training of all atomic species in the data set. We demonstrate that the accuracy of the developed approach in representing both chemical and configurational spaces is comparable to the one of several established machine learning models. Due to its high accuracy and efficiency, the proposed machine-learned potentials can be used for any further tasks, for example the optimization of molecular geometries, the calculation of rate constants or molecular dynamics.