Learning and Learning to Solve PDEs

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 impact of deep learning on computational mathematics. I will present our recent work on bridging deep neural networks with numerical differential equations. On the one hand, I will show how to design transparent deep convolutional networks to uncover hidden PDE models from observed dynamical data. On the other hand, I will present our preliminary attempt to establish a deep reinforcement learning based framework to solve 1D scalar conservation laws, and a meta-learning approach for solving linear parameterized PDEs based on the multigrid method.

data structures and algorithmsmachine learningmathematical physicsinformation theoryoptimization and controldata analysis, statistics and probability

Audience: researchers in the topic

( video )

Mathematics, Physics and Machine Learning (IST, Lisbon)

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Zoom link: videoconf-colibri.zoom.us/j/91599759679