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Provable Size Requirements for Operator Learning and PINNs

Series: Bangalore Theory Seminars

Speaker: Anirbit Mukherjee, University of Manchester

Date/Time: Aug 27 16:00:00

Location: Online talk-teams link follows

Abstract:
An ongoing revolution in machine learning is about being able to set up neural systems that can approximate maps between Banach spaces. The most basic such setup is that of Deep Operator Nets (DeepONets). We will begin this talk by introducing this fascinating idea and how it leads to a mechanism of using machine learning to solve systems of Partial Differential Equations. Next, we will focus on our recent work proving -universal-/data-independent size requirements for DeepONets, for them to be able to perform well. We will emphasize the modularity of the proof structure and why its readily adaptable to many other ML systems. Thus, we pave the path towards a plethora of research avenues for deriving model size requirements for many other ML scenarios.


This talk is largely based on our work with Amartya Roy (now a PhD student at IIT-Delhi), published in Transactions in Machine Learning (TMLR) in 2024, Link Towards the end, we will touch upon the following work, Link where a similar result was obtained for PINNs, with my PhD student Sebastien Andre-Sloan and Prof. Matthew Colbrook (DAMTP, Cambridge).


Microsoft teams link:

Link

We are grateful to the Kirani family (Link and the Walmart Center for Tech Excellence (Link for generously supporting this seminar series


Hosts: Nirjhar Das, Rameesh Paul, KVN Sreenivas, Rahul Madhavan, Debajyoti Kar