Challenges and prospects of a posteriori error estimation in density-functional theory

Last week Wednesday I was invited to give a talk at the group seminar of the AG Christoph Jacob at TU Braunschweig, Germany. Christoph was especially interested in our recent publication on a posteriori error estimation in Kohn-Sham problems and so I decided to use the opportunity to give a broad introduction into the topic. Since the main audience for my talk were chemists I motivated our work from the context of high-throughput density-functional theory calculations, which are becoming more and more of interest in practice. In the second part of my talk I tried to lay out the basic ideas and challenges of a posteriori error estimation and what are the key aspects to understand and overcome if one wants to provide a useful error bound for a particular problem (see also this article for more details). In the last part of the talk I turned the attention specifically to our recent contribution, discussing error estimates in the context of simple Kohn-Sham problems. Many of the delicate details of our work I did not touch upon, but nevertheless this last section of my talk gives a very good overview of our approach, our main underlying assumptions and our results. While we have focused solely on plane-wave basis sets in our work, I briefly hinted whether extensions to other basis sets with similar methods can be achieved.

Unfortunately the whole "visit" to Braunschweig was completely virtual, which really was a shame as I would have loved to return to the city and spend a day with the group. Despite these circumstances though the discussions with Christoph and his group did not not really fall short. During the day I had many video call sessions where I had ample opportunity to discuss with PhD students about their projects and in this way get a good idea of the interesting research going on in Braunschweig. As that's typically my favourite part about visiting a group I'm very happy this worked out so well (thanks to everyone who I managed to talk to!) and I already look forward to properly meeting everyone in person when the usual conference schedules are back in place.

The slides from my talk are attached below.

Challenges and prospects of a posteriori error estimation in density-functional theory (Slides)