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The construction of a better exchange-correlation potential in time-dependentdensity functional theory (TDDFT) can improve the accuracy of TDDFTcalculations and provide more accurate predictions of the properties ofmany-electron systems. Here, we propose a machine learning method to developthe energy functional and the Kohn-Sham potential of a time-dependent Kohn-Shamsystem is proposed. The method is based on the dynamics of the Kohn-Sham systemand does not require any data on the exact Kohn-Sham potential for training themodel. We demonstrate the results of our method with a 1D harmonic oscillatorexample and a 1D two-electron example. We show that the machine-learnedKohn-Sham potential matches the exact Kohn-Sham potential in the absence ofmemory effect. Our method can still capture the dynamics of the Kohn-Shamsystem in the presence of memory effects. The machine learning method developedin this article provides insight into making better approximations of theenergy functional and the Kohn-Sham potential in the time-dependent Kohn-Shamsystem.

Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems