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Title: | PolyU 85th and AMA 50th anniversary distinguished lecture : Deep adaptive sampling for numerical PDEs | Other Title: | Deep adaptative sampling for numerical PDEs | Authors: | Tang, Tao | Issue Date: | 2022 | Abstract: | Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.<br>Event date: 18/10/2022<br>Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)<br>Hosted by: Department of Applied Mathematics | Keywords: | Sampling (Statistics) Differential equations, Partial -- Numerical solutions Mathematical models Adaptive computing systems |
Publisher: | Hong Kong Polytechnic University |
Appears in Collections: | Open Educational Resources |
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