Speaker: Handi Zhang

Abstract: Scientific machine learning (SciML) has become a popular area of research in recent years, with applications in a wide range of fields such as physics, biology, and engineering. One of the key challenges in SciML is the need to learn complex nonlinear operators.  In this seminar, I’ll explore the concept of operator learning in SciML and provide an overview of how neural operators, such as Deep Neural Operators (DeepONets) and Fourier Neural Operators (FNOs) are designed to learn different types of operators. Then I will quickly review some theories of neural operators, including approximation theorem, error estimate and convergence analysis. In this end, I will introduce applications of neural operators in various fields and highlight some of the ongoing challenges in this area.