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

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/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, we examine the use of FNOs in addressing the density-to-potential inversion problem in static DFT. By employing these methods as alternatives to numerical inversion schemes, we demonstrate enhancements in predictive transferability and speed. We highlight the applications to exactly solvable systems, illustrating their potential as accurate and rapid data-driven surrogate models.  

In the second part, we discuss the application of PINNs to accelerate TDDFT calculations. By incorporating the fundamental physical constraints of the TD 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 ML, these projects shed light on promising new directions for addressing challenges in DFT and TDDFT, enabling the simulation of electron dynamics across larger scales and under extreme conditions.