# TrAC seminar: Learning Operators

**Author: Lona**

**Author: Lona**

**Speaker:** Siddhartha Mishra, Professor of Mathematics at the Seminar for Applied Mathematics at ETH Zürich

**Abstract:** Operators are mapping between infinite-dimensional spaces and arise in a variety of contexts, particularly in the solution of PDEs. The main aim of this lecture would be to introduce the audience to the rapidly emerging area of operator learning, i.e., machine learning operators from data. To this end, we will summarize existing architectures such as DeepONets and Fourier neural operators (FNOs) as well as describe the newly proposed Convolutional Neural Operators (CNOs). Theoretical error estimates for different operator learning architectures will be mentioned and numerical experiments comparing them described. Several open issues regarding operator learning will also be covered. If time permits, we will describe Neural Inverse operators (NIOs): a machine-learning architecture for the efficient learning of a class of inverse problems associated with PDEs.

**Short Bio:**

Siddhartha Mishra is a professor at the Seminar for Applied Mathematics and head of the Computational and Applied Mathematics Laboratory (CAMLab). Prof. Siddhartha Mishra received an honors degree in Mathematics and Physics from Utkal University in Bhubaneswar in 2000. After his graduation he joined the Applied Mathematics program run jointly by IISc and TIFR in Bengaluru. By 2005 he had earned both an M.S. and Ph.D. degrees from both. Prof. Mishra went to CMA at University of Oslo as a post-doc (2005-2009) and followed it up with an Assistant Professorship at ETH Zürich (2009-2011). He returned briefly to Oslo for a year and then went back to Zürich in 2012 as an Associate Professor and became a full Professor in 2015. Mishra is the recipient of many awards such as the Richard von Mises Prize (2015), the Jacques Louis Lions Award (2018), and the ICIAM Collatz Prize (2019). He was an invited speaker at the International Congress of Mathematicians held in Rio de Janeiro in 2018.