arXiv subjects

Bhupalee Kalita

Publications and source records attributed to Bhupalee Kalita.

4 recordsLinked to original sources

arXiv2023

Seven Useful Questions in Density Functional Theory

We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing computations using density functional theory. Subjects covered include the magnitude of the kinetic energy in Hartree-Fock calculations, the shape of adiabatic connection curves, using the constrained search with input densities, densities of states, the semiclassical expansion of energies, the tightness of Lieb-Oxford bounds, and how we decide the accuracy of an approximate density.

math-ph↗

arXiv2022

Machine learning and density functional theory

Over the past decade machine learning has made significant advances in approximating density functionals, but whether this signals the end of human-designed functionals remains to be seen. Ryan Pederson, Bhupalee Kalita and Kieron Burke discuss the rise of machine learning for functional design.

physics.comp-ph↗

arXiv2022

How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?

Kohn-Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn-Sham density functional theory (DFT) that works for strongly correlated systems. Here we test KSR for weak correlation. We propose spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations found by minimizing density and total energy loss. We assess the atoms-to-molecules generalizability by training on one-dimensional (1D) H, He, Li, Be, Be$^{++}$ and testing on 1D hydrogen chains, LiH, BeH$_2$, and helium hydride complexes. The generalization error from our semilocal approximation is comparable to other differentiable approaches, but our nonlocal functional outperforms any existing machine learning functionals, predicting ground-state energies of test systems with a mean absolute error of 2.7 milli-Hartrees.

physics.chem-ph↗

arXiv2021

Using Machine Learning to Find New Density Functionals

Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the status of this field and point out some current and future challenges. We also talk about how state-of-the-art science and technology tools can help overcome these challenges. This draft is a part of the "Roadmap on Machine Learning in Electronic Structure" to be published in Electronic Structure (EST).

physics.chem-ph↗