Wednesday, August 10, 2022 - 3:00pm

Abstract: Density functional theory (DFT), combined with standard exchange-correlation (XC) approximations, is a usefully accurate and efficient tool for computational predictions in chemistry and material sciences. By building physics-informed machine learning (ML) approximations for the XC energy functional, the accuracy of DFT calculations can be improved further. The Kohn-Sham regularizer (KSR) is a differentiable approach for solving the Kohn-Sham equations in DFT while approximating the XC functional with ML. Part of this thesis work discusses the spin-adapted implementation of KSR with modified local, semilocal, and nonlocal neural network model approximations for the XC energy functional. The proposed nonlocal XC approximation can predict the ground-state properties of a set of 1D equilibrium-bonded molecules with near chemical accuracy when trained on just a handful of 1D atomic systems. Such atoms-to-molecules generalization can pave the way for a practical, highly-accurate ML functional approximation.

We can also use machine learning to characterize human-designed XC functionals. Debates abound over which of the hundreds of XC approximations are best or even on what basis to judge. We also propose an unsupervised learning scheme in this thesis to group XC functionals without considering any absolute errors in the functionals. We introduce a measure of distinction between approximate functionals,  the density-driven fractional difference (DDF), based on density-corrected DFT, and evaluate this functional fingerprint for the MGAE109 dataset from the Minnesota database for 33 popular XC approximations. We construct a matrix space using these fingerprints and evaluate the similarities among the functionals using a novel parameter-free unsupervised learning algorithm. In the DDF feature space, this algorithm creates functional categories that largely (but not entirely) mimic those based on their ingredients, analogous to the famous Jacob’s ladder categorization. Finally, we illustrate these functional clusters using various popular dimensionality reduction tools. Our scheme shows, in agreement with earlier speculation, that specific construction techniques of approximate functionals yield approximations that differ wildly from more established XC functionals.

Speaker: 

Bhupalee Kalita

Institution: 

Burke Group

Location: 

NS2 2201