Predicting electron dynamics in proton-irradiated small molecules by recurrent neural networks

We demonstrate the application of recurrent neural networks toward learning the real-time electron dynamics of small organic molecules irradiated by fast protons. Real-time time-dependent density functional (RT-TDDFT) theory is a powerful method to capture full time dependence of electronic excitations due to motion of fast H+ ions (at the order of 1.0 Bohr velocity). However, the computational costs becomes prohibitively expensive with the combinatorial space of molecular targets, proton trajectories, and range of speeds. We show that the required number of RT-TDDFT simulations can be minimized by incrementally adding more speed-trajectory combinations selected by an active learning loop. Once trained, recurrent neural networks (RNNs) are able to predict the time dependent change in orbital occupation number with mean absolute errors of 0.04 electrons for speed-trajectory combinations not used in model training. The RNNs show a limited ability to extrapolate to molecular targets not included in the training set. Our approach developed in this work shows potential to vastly accelerate the study of time dependent electronic excitations by using RNN models to reduce the number of RT-TDDFT calculations required to fully examine irradiation processes. Furthermore, our approach opens the opportunity for future multi-scale simulations of electron-ion dynamics in molecules irradiated by ion beams.