Artificial Intelligence for Mathematics

Abstract: Novel approaches based on artificial intelligence have already shown their impressive potential in mathematical research areas such as imaging sciences or numerical analysis of partial differential equations, sometimes by far outperforming classical mathematical approaches for particular problem classes.

In this second lecture, we will focus on optimal combinations of traditional model-based methods with AI-based approaches in the sense of true hybrid algorithms for imaging sciences. In this realm, we will present some recent advances for the ill-posed problems of (limited-angle) computed tomography and shape reconstruction. Finally, we will also touch upon mathematical insights into the ability of deep neural networks to circumvent the curse of dimensionality for high-dimensional partial differential equations and their benefits as solvers.

Mathematics

Audience: researchers in the topic

UCLA distinguished lecture series

Series comments: Description: Lectures by distinguished mathematicians, hosted at UCLA

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.