Feed-forward neural networks for fitting of kinetic energy and its functional derivative

Abstract

We present a feed-forward NN approach for fitting of kinetic energy and its functional derivative for a 1-dimensional system. The density is represented in terms of orthogonal basis functions. The coefficients of basis functions forms the inputs to NN. Using this approach we found no oscillatory behaviour in functional derivative. Using NN based functional derivative we determine the ground-state density by solving the Euler–Lagrange equation. The presented approach can open up new ways for accurate calculations kinetic energy and the functional derivative, which can be considered as an important step towards advancement of machine learning based OF-DFT methods.