CMX Student/Postdoc Seminar

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 is still in its infancy; Why are neural networks so effective in these applications? In this talk, I will discuss work addressing what neural networks can and cannot achieve in this context.