SFU MOCAD Seminar: Harish S. Bhat

To compute the quantum dynamics of a molecule's electrons, one tractable way to proceed is via time-dependent density functional theory (TDDFT). TDDFT gives equations of motion that, in principle, yield the same electron density as the full but intractable time-dependent Schrodinger equation. However, there is one term in the TDDFT Hamiltonian whose functional form is unknown: the exchange-correlation potential (Vxc). This motivates the idea of trying to learn Vxc (or, at least, an improved model of Vxc) from data. I will review progress on this problem that includes (i) generation of suitable training data, (ii) direct learning of Vxc neural network models in one spatial dimension, and (iii) PDE-constrained optimization techniques to learn Vxc in two spatial dimensions. A key ingredient in (ii) and (iii) will be the adjoint method, which connects our work to quantum optimal control. We will conclude by briefly describing how to use the adjoint method (together with small neural networks) to solve quantum optimal control problems for molecules driven by electric fields.