Despite the outstanding success of artificial intelligence (AI) in real-world applications, most of the related research is empirically driven and a comprehensive theoretical foundation is still missing. At the same time, AI-based methods have already shown their impressive potential in research areas closely related to physical models, such as inverse problems or numerical analysis of partial differential equations, sometimes by far outperforming the then-status-quo of classical solvers.
In this talk we will first provide an introduction into this research area. We will then discuss selected classes of deep learning-based solvers for operator equations and also provide numerical examples, in particular, for computed tomography and parametric PDEs. Finally, we will touch upon the question of how those results can be theoretically
Online via ZOOM:
Meeting ID: 984 5733 2925
Peter Thirolf (LMU) / Norbert Kaiser (TUM)