Abstract

Deep learning continues to dominate machine learning and has been successful in computer vision, natural language processing, etc. Its impact has now expanded to many research areas in science and engineering. In this talk, I will mainly focus on some recent impacts of deep learning on computational mathematics. I will present our recent work on bridging deep neural networks with numerical differential equations, and how it may guide us in designing new models and algorithms for some scientific computing tasks. On the one hand, I will present some of our works on the design of interpretable data-driven models for system identification and model reduction. On the other hand, I will present our recent attempts at combining wisdom from numerical PDEs and machine learning to design data-driven solvers for PDEs and their applications in electromagnetic simulation.