Applied Math Colloquium: Ke Chen
Wednesday, February 7, 2024 · 12 - 1 PM
Title: Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms
Speaker: Ke Chen (University of Maryland, College Park)
Abstract: Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in scientific computing. This talk delves into efficient training for PDE operator learning in both the forward and inverse PDE settings. Firstly, we address the curse of dimensionality in PDE operator learning, demonstrating that certain PDE structures require fewer training samples through an analysis of learning error estimates. Secondly, we introduce an innovative DNN, the pseudo-differential auto-encoder integral network (pd-IAE net), and compare its numerical performance with baseline models on several inverse problems, including optical tomography and inverse scattering. We will briefly mention some future works at the end, focusing on the regularization of inverse problems in the context of operator learning.
