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.

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