Physics-Informed Machine Learning for Addressing Challenges in Static and Time-Dependent Density Functional Theory

In this talk, we explore the potential of Physics-Informed Machine Learning (ML) in addressing
key computational tasks in both static and time-dependent Density Functional Theory (DFT
and TDDFT). The talk will focus on two projects that employ advanced ML techniques,
specifically Physics-Informed Neural Networks (PINNs) and Fourier Neural Operators (FNOs),
to tackle these complex tasks.
In the first part of the presentation, we examine the use of PINNs and FNOs in addressing the
intricate density-to-potential inversion problem in static DFT. By employing these methods as
alternatives to conventional inversion schemes, we demonstrate enhancements in predictive
transferability and speed. We highlight the applications to exactly solvable models, such as
soft-Coulomb systems, illustrating their potential as accurate and rapid data-driven surrogate
models.
In the second part of the talk, we discuss the application of PINNs to accelerate TDDFT
calculations. By incorporating the fundamental physical constraints of the Time-Dependent
Kohn-Sham equations directly into the learning process, PINNs offer a unique way to fuse the
power of deep learning with the nuances of TDDFT. We demonstrate the performance and
generalisability of PINN solvers on the time evolution of model systems across varying system
parameters, domains, and energy states.
By integrating physics and machine learning, these projects shed light on promising new
directions for addressing challenges in DFT and TDDFT. The methods developed here have
the potential to accelerate (TD)DFT workflows, enabling the simulation of large-scale
calculations of electron dynamics in matter exposed to strong electromagnetic fields, high
temperatures, and pressures.