Paris Perdikaris: A Unifying Framework for Operator Learning via Neural Fields

01 December 2023 15:00 till 16:00 - Location: building 36 EEMCS, Elektron room, HB 01.230 | Add to my calendar

Operator learning is an emerging area of machine learning which aims to learn mappings between infinite dimensional function spaces and has led to the development of new architectures such as the Fourier Neural Operator, the DeepONet, and their extensions.
In this talk I will uncover a previously unrecognized connection between existing operator learning architectures and conditioned neural fields used in computer vision.
This results in a unified framework for explaining differences between popular operator learning architectures, and creates a bridge for adapting well-developed tools from computer vision for operator learning. In particular, we find all existing operator learning architectures are neural fields whose conditioning mechanisms are restricted to use only pointwise and/or global information. This motivates us to design new architectures which make use of a hierarchy of scales for conditioning a base neural field. By making use of multi-scale conditioning, we observe consistent performance gains and obtain state of the art results across a collection of challenging benchmarks in climate modelling and fluid dynamics.