Development of new and highly accurate density functionals with machine learning
Prof Marivi Fernandez-Serra, Institute for Advanced Computational Sciences and Physics and Astronomy Department, Stony Brook University
Density functional theory (DFT) serves without doubt as the workhorse method for electronic structure simulations in materials science and physics and has gained popularity within the chemistry community in recent decades. This is in no small part due to its favorable scaling, allowing users to tackle system sizes out of reach for most correlated wavefunction methods.
However, inferences made from numerical simulations are only ever as good as their underlying approximations. This remains true for DFT, where these approximations are bundled somewhat opaquely in the elusive exchange-correlation (XC) functional. The Hohenberg-Kohn theorem guarantees that if this functional were known, ground-state properties of any interacting many-electron system could be described exactly. In practice, one needs to pick from a plethora of different approximations, which often boils down to finding the right functional, cost and accuracy-wise, for the problem at hand.
In this work, using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain a highly accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that at the meta-GGA level our functional exhibits unprecedented accuracy for both energy and density predictions.