Assad Oberai, University of Southern California
Daniel Huang, California Institute of Technology
Lu Lu, University of Pennsylvania
Dhruv Patel, Stanford University
Paris Perdikaris, University of Pennsylvania
Deep Ray, University of Southern California
Yue Yu, Lehigh University
The last few years have witnessed a rise in the popularity of deep learning-based surrogate models to solve partial differential equations (PDEs). In particular, operator networks, which approximate the solution operator of the PDE, have shown great promise in various problems in science and engineering. Several flavors of operator networks are currently available, such as DeepONets, Fourier Neural Operators and Graph Neural Operators, each with their own set of advantages in terms of ease in training and accompanying theoretical analysis. These differentiable surrogate models can play a big role improving the computational efficiency of many-query downstream tasks, which include PDE-constrained optimization, inverse problems, and uncertainty quantification.
This symposium brings together researchers to share some recent progress and their perspectives on (i) the methodology development of deep learning surrogate models for PDE-based problems, (ii) existing theory and mathematical interpretation of these approaches, and iii) challenges in deploying such strategies to solve large-scale problems.