Speaker: Dr. Lu Lu from Brown University (hosted by Xingjie Li).
Title: Learning dynamical systems and differential equations with deep learning: physics-informed and data-driven
Abstract: Deep learning has achieved remarkable success in diverse applications; however, its use in learning dynamical systems and partial differential equations (PDEs) has emerged only recently. These learning approaches can be either physics-informed or data-driven. In the physics-informed approach, I have improved the physics-informed neural networks (PINNs) and developed the library DeepXDE for solving different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. In the data-driven approach, I have developed the deep operator network (DeepONet) based on the universal approximation theorem of operators to learn dynamical systems accurately and efficiently from a relatively small dataset. In addition, I will present my work on the deep learning theory of optimization and generalization, and the application of applying multi-fidelity neural networks to predict mechanical properties of solid materials.