The 40th Anniversary of Shenzhen University and the 40th Anniversary of Mathematics Department

Liyuan scholar Colloquiumfifty-five

Title: Deep Operator-Splitting Network (DOSnet) for Solving PDEs

Speaker：Prof. Xiang Yang (Hong Kong University of Science and Technology)

Lecture time：December 1, 2023, 10:00-11:00 a.m.

Lecture location:Classroom No. 4, 1/F, Hui Xing Building, Yuehai Campus, Shenzhen University, China

Overview：Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning based solvers utilize the representation power of DNNs to approximate the input-output relations in an automated manner. However, the lack of physics-in-the-loop often makes it difficult to construct a neural network solver that simultaneously achieves high accuracy, low computational burden, and interpretability. In this work, focusing on a class of evolutionary PDEs characterized by decomposable operators, we show that the classical operator splitting technique can be adapted to designing neural network architectures. This gives rise to a learning-based PDE solver, which we name Deep Operator-Splitting Network (DOSnet). Such non-black-box network design is constructed from the physical rules and operators governing the underlying dynamics, and is more efficient and flexible than the classical numerical schemes and standard DNNs. To demonstrate the advantages of our new AI-enhanced PDE solver, we train and validate it on several types of operator-decomposable differential equations. We also apply DOSnet to nonlinear Schrodinger equations which have important applications in the signal processing for modern optical fiber transmission systems, and experimental results show that our model has better accuracy and lower computational complexity than numerical schemes and the baseline DNNs.

Speaker Introduction：Prof. Yang Xiang is a Professor in the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST), where he received his Ph.D. from the Crown Institute of Mathematics at New York University in 2001, and did postdoctoral work at Princeton University from 2001 to 2003 before joining the Department of Mathematics at HKUST in 2003. His main research interests lie in mathematical modeling, numerical computation, and corresponding analysis in materials science, and he has achieved a series of original results of great significance in materials modeling and computation related to defects. He is a conference presenter of the American Society for Industrial and Applied Mathematics Conference on Mathematical Problems in Materials Science 2021, and was selected as one of the Top 2% scientists in the world released by Stanford University in 2021 and 2022. He is currently the President of the East Asian Society for Industrial and Applied Mathematics.

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Teachers and students are welcome to participate!

School of Mathematical Sciences

November 27, 2023