  Photo-induced processes are fundamental in nature, but accurate simulations
are seriously limited by the cost of the underlying quantum chemical
calculations, hampering their application for long time scales. Here we
introduce a method based on machine learning to overcome this bottleneck and
enable accurate photodynamics on nanosecond time scales, which are otherwise
out of reach with contemporary approaches. Instead of expensive quantum
chemistry during molecular dynamics simulations, we use deep neural networks to
learn the relationship between a molecular geometry and its high-dimensional
electronic properties. As an example, the time evolution of the
methylenimmonium cation for one nanosecond is used to demonstrate that machine
learning algorithms can outperform standard excited-state molecular dynamics
approaches in their computational efficiency while delivering the same
accuracy.
