Einladung zum Statusvortrag im Promotionsver­fahren von Herrn Karan Shah

Abstract:

Physics-informed machine learning (PIML) is a rapidly growing area of research that fuses ML models with physics-based constraints. It has a wide range of applications in scientific computing, in fields such as fluid dynamics, climate modeling, and plasma physics.

These models are used for two broad classes of problems: forward modeling and  inverse modeling. Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs) have been used for forward modeling problems such as simulating turbulent fluid flow and for inverse modeling problems such as seismic waveform inversion. 

We adapt and apply these algorithms to the field of electronic structure calculations based on Density Functional Theory (DFT) which is the most widely used method to study the electronic structure and dynamics of many-body systems.

For the forward modeling problem, we demonstrate the effectiveness of PIML methods in the context of time-dependent DFT. We show that PIML models with constraints based on the underlying Kohn-Sham equations provide good generalizability and high accuracy while accelerating real-time TDDFT calculations.

For the inversion problem, we consider DFT inversions which are used to extract the effective potential of the single-particle Kohn-Sham system from target electron densities. This ill-posed problem is computationally demanding and challenging to generalize across different systems. We develop NO-based inversion models and demonstrate their effectiveness against standard numerical methods and other PIML techniques, such as PINNs.