By-passing the Kohn-Sham equations with machine learning

Kohn-Sham density functional theory[1] is now enormously popular as an electronic structure method in a wide variety of fields[2]. Useful accuracy is achieved with standard exchange-correlation approximations, such as generalized gradient approximations[3] and hybrids[4]. Such calculations are playing a key role in the materials genome initiative[5], at least for weakly correlated materials[6]. There has also been a recent spike of interest in applying machine learning (ML) methods in the physical sciences[7-11]. The majority of these applications involve predicting properties of molecules or materials from large databases of KS-DFT calculations[12-15]. A few applications involve finding potential energy surfaces within MD simulations[16-19]. Fewer still have focussed on finding the functionals of DFT as a method of performing KS electronic structure calculations without solving the KS equations[20-23]. If such attempts could be made practical, the possible speedup in repeated DFT calculations of similar species, such as occur in ab initio MD simulations, is enormous. A key difficulty has been the need to extract the functional derivative of the non-interacting kinetic energy.