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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 dynamic systems, especially partial differential equations (PDEs). On the one hand, I will show how to tackle inverse problems by designing transparent deep convolutional networks to uncover hidden PDE models from observed dynamical data; to combine the wisdom from mathematical algorithms with ideas from deep learning to improve image restoration. On the other hand, I will discuss how deep learning may improve numerical PDE solvers. I will present one of our recent works that suggests a meta-learning approach to improve the multigrid method for solving linear parameterized PDEs. |