Machine learning powered kinetic energy functional finding in solid state physics

Kinetic energy functional is crucial to speed up the density functional theory calculation. However, deriving it directly from first principle is challenging, and existing approximations all have significant flaw. In this work, we use machine learning method to build a kinetic energy functional for 1D extended system, our solution combines the dimensionality reduction method with the Gauss process regression, and use a simple scaling trick to generalize the functional to 1D lattice with arbitrary lattice constant. Besides reaching chemical accuracy in kinetic energy calculation, our solution also performs well in functional derivative prediction, and integrating it into the current orbital free density functional theory scheme provide us with expected ground state electron density.