Abstract: Kohn-Sham density-functional theory (DFT) is a widely employed physical model for first-principles materials simulation. Despite the significant mathematical complexity --- a non-linear model with a non-smooth objective --- robust algorithms exist for solving the forward problem:
predicting physical properties from input parameters such as material structure or model choices. In contrast, the inverse problem --- inferring structural or model parameters from observed physical properties --- remains comparatively unexplored, lacking both a strong mathematical foundation and robust algorithmic solutions. This talk will present recent research on solving inverse problems in DFT, focusing on a novel algorithm for density-potential inversion, where we have developed first-order a posteriori error bounds. These developments are implemented within the density-functional toolkit (DFTK), a Julia-based package enabling rapid prototyping of DFT simulations and supporting advanced mathematical research with high-performance computing capabilities.
This is joint work with Niklas Schmitz (EPFL) as well as Vebjørn H. Bakkestuen and Andre Laestadius (both OsloMet University).
I am a tenure-track assistant professor at EPFL with a joint appointment in the Maths and Materials Science institutes.
I run the Mathematics for Materials Modelling research group, where our main interest is the understanding of simulation errors in materials modelling and the development of robust black-box algorithms. In our work we take an interdisciplinary viewpoint somewhere at the boundary of mathematics, solid-state physics and computer science.
