Reproducing global potential energy surfaces with continuous-filter convolutional neural networks

Neural networks fit to reproduce the potential energy surfaces of quantum chemistry methods offer a realization of analytic potential energy surfaces with the accuracy of ab initio methods at a computational cost similar to classical force field methods. One promising class of neural networks for this task is the SchNet architecture, which is based on the use of continuous-filter convolutional neural networks. Previous work has shown the ability of the SchNet architecture to reproduce density functional theory energies and forces for molecular configurations sampled during equilibrated molecular dynamics simulations. Due to the large change in energy when bonds are broken and formed, the fitting of global potential energy surfaces is normally a more difficult task than fitting the potential energy surface in the region of configurational space sampled during equilibrated molecular dynamics simulations. Herein, we demonstrate the ability of the SchNet architecture to reproduce the energies and forces of the potential energy surfaces of the H + H₂ and Cl + H₂ reactions and the OCHCO⁺ and H₂CO/cis-HCOH/trans-HCOH systems. The SchNet models reproduce the potential energy surface of the reactions well with the best performing SchNet model having a test set root-mean-squared error of 0.52 meV and 2.01 meV for the energies of the H + H₂ and Cl + H₂ reactions, respectively, and a test set mean absolute error for the force of 0.44 meV/bohr for the H + H₂ reaction. For the OCHCO⁺ and H₂CO/cis-HCOH/trans-HCOH systems, the best performing SchNet model has a test set root-mean-squared error of 2.92 meV and 13.55 meV, respectively.