Neural networks have proven to be effective approximators of high dimensional functions in a wide variety of
applications. In scientific computing the goal is often to approximate an underlying operator, which defines a
mapping between infinite-dimensional spaces of input and output functions. Extensions of neural networks to this infinite-dimensional setting have been proposed in recent years, giving rise to the emerging field of operator learning. Despite their practical success, our theoretical understanding of these approaches remains incomplete; Why are neural networks so effective in these applications? In this talk, I will discuss recent work on the approximation theory underpinning operator learning. This work aims to address what can and cannot be achieved in this context.
Learning operators with neural networks
10.06.2024 09:50 - 10:35
Organiser:
Fakultät für Mathematik, Dekan Radu Ioan Boţ
Location: