Room: 5-314
Speaker Name:
Paris Perdikaris
Affiliation:
University of Pennsylvania – Department of Mechanical Engineering and Applied Mechanics &
Principal Researcher at Microsoft Research AI4Science
Abstract:
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 weather modelling and fluid dynamics.
*joint work with Jacob Seidman, Hanwen Wang, Shyam Sankaran and George Pappas
Biography:
Paris Perdikaris is an Associate Professor in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania and a Principal Researcher at Microsoft Research AI4Science. He received his PhD in Applied Mathematics at Brown University in 2015, and, prior to joining Penn in 2018, he was a postdoctoral researcher at the department of Mechanical Engineering at the Massachusetts Institute of Technology. His current research interests include physics-informed deep learning, generative models and uncertainty quantification with applications to simulating and optimizing physical and engineering systems.