The Mathematics of Artificial Intelligence

Ponente(s): Gitta Kutyniok

Artificial intelligence is currently leading to one breakthrough after the other, both in public life with, for instance, autonomous driving and speech recognition, and in the sciences in areas such as medical diagnostics or molecular dynamics. A similarly strong impact can currently be witnessed within mathematics on areas such as inverse problems and numerical analysis of partial differential equations. The goal of this lecture is to first provide an introduction into this new vibrant research area. We will then survey recent advances in two directions, namely the development of a mathematical foundation of artificial intelligence and the introduction of according novel approaches to solve inverse problems and partial differential equations. We will also discuss fundamental limitations of such methodologies, in particular, in terms of computability.