Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative

Orbital-free
approaches might offer a way to boost the applicability
of density functional theory by orders of magnitude in system size.
An important ingredient for this endeavor is the kinetic energy density
functional. Snyder et al. [Phys. Rev. Lett. 2012, 108, 253002] presented a machine
learning approximation for this functional achieving chemical accuracy
on a one-dimensional model system. However, a poor performance with
respect to the functional derivative, a crucial element in iterative
energy minimization procedures, enforced the application of a computationally
expensive projection method. In this work we circumvent this issue
by including the functional derivative into the training of various
machine learning models. Besides kernel ridge regression, the original
method of choice, we also test the performance of convolutional neural
network techniques borrowed from the field of image recognition.