Prachi Gupta

Harish S. Bhat, Kevin Collins, Prachi Gupta et al.

We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrödinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.

Arka Talukdar, Monika Dagar, Prachi Gupta et al.

The recent increase in dataset size has brought about significant advances in natural language understanding. These large datasets are usually collected through automation (search engines or web crawlers) or crowdsourcing which inherently introduces incorrectly labeled data. Training on these datasets leads to memorization and poor generalization. Thus, it is pertinent to develop techniques that help in the identification and isolation of mislabelled data. In this paper, we study the applicability of the Area Under the Margin (AUM) metric to identify and remove/rectify mislabelled examples in NLP datasets. We find that mislabelled samples can be filtered using the AUM metric in NLP datasets but it also removes a significant number of correctly labeled points and leads to the loss of a large amount of relevant language information. We show that models rely on the distributional information instead of relying on syntactic and semantic representations.

Prachi Gupta, Harish S. Bhat, Karnamohit Ranka et al.

We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.