Title:     Learning Nonlinear Operators Using Deep Neural Networks for Diverse Applications

Speaker:     Dr. Lu Lu, University of Pennsylvania

Abstract:     It is widely known that neural networks (NNs) are universal approximators of continuous functions.  However, a less known but powerful result is that a NN can accurately approximate any nonlinear continuous operator.  This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data.  In this talk, I will present the deep operator network (DeepONet) to learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations.  More generally, DeepONet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously.  We will demonstrate the effectiveness of DeepONet to multiphysics and multiscale problems.