  We propose a machine learning based approach to develop the
exchange-correlation potential of time dependent density functional theory
(TDDFT). The neural network projection from the time-varying electron densities
to the corresponding correlation potentials in the time-dependent Kohn-Sham
equation is trained using a few exact datasets for a model system of
electron-hydrogen scattering. We demonstrate that this neural network potential
can capture the complex structures in the time-dependent correlation potential
during the scattering process and provide correct scattering probabilities,
which are not obtained by the standard adiabatic functionals. We also show that
it is possible to incorporate the nonadiabatic (or memory) effect in the
potential with this machine learning technique, which significantly improves
the accuracy of the dynamics. The method developed here offers a novel way to
improve the exchange-correlation potential of TDDFT, which makes the theory a
more powerful tool to study various excited state phenomena.
