Inaugural lecture: Robust error-controlled materials simulations

Systematic first-principle simulations are nowadays a key component when developing novel materials. Usually the resulting simulation data is not directly used to drive the search, but instead employed to train a considerable cheaper statistical surrogate.  In this setting of potentially millions of simulations as well as these multiple layers of approximations (physical, numerical, statistical) obtaining robust computational workflows and tracking simulation errors remains challenging.

In this talk I will report on progress along two axes of research to tackle these challenges.  The first concerns the development of robust numerical algorithms for density-functional theory (DFT) --- the most widely employed family of first-principle models in the field. The focus of the development here is to obtain black-box methods that are able to automatically adapt to the physics of the simulated system. Secondly, I will discuss first results on employing multi-task statistical surrogate models, a surrogatisation technique, which enables the use of data of heterogeneous quality when training a single surrogate. By combining materials simulation approaches of different cost/accuracy balances this not only unlocks computational savings to generate training data, but also allows to opportunistically exploit heterogeneous databases of already existing simulation data.

In both efforts software has played a key role to provide an accessible platform fostering such interdisciplinary developments. In our work we develop and extend the density-functional toolkit (DFTK), a Julia-based DFT code, suitable to mathematical research (only 7500 lines of code), but at the same time integrated into standard tools for materials discovery such as AiiDA.

Bio: Michael Herbst obtained a PhD in Theoretical Chemistry from Heidelberg University in 2018, after which he moved on to two postdoctoral research stays in Applied Mathematics. From 2019 till 2021 he worked with Éric Cancès (École des Ponts, Paris, France) and from 2021 till 2023 he stayed in the group of Benjamin Stamm (RWTH Aachen). Since March 2023 he is an assistant professor in the Institute of Mathematics and the Institute of Materials at EPFL. His current research spans broadly in the field of materials simulations concerning numerical error control and uncertainty quantification of DFT models as well as the development of efficient and robust algorithms for high-throughput materials screening.