Towards the construction of an accurate kinetic energy density functional and its functional derivative through physics-informed neural networks

One of the primary obstacles in the development of orbital–free density functional theory is the lack of an accurate functional for the Kohn–Sham non-interacting kinetic energy, which, in addition to its accuracy, must also render a good approximation for its functional derivative. To address this critical issue, we propose the construction of a kinetic energy density functional throught physical- informed neural network, where the neural network’s loss function is designed to simultaneously reproduce the atom’s shell structures, and also, an analytically calculated functional derivative. As a proof-of-concept, we have tested the accuracy of the kinetic energy potential by optimizing electron densities for atoms from Li to Xe.