深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第五十五期

讲座题目: Deep Operator-Splitting Network (DOSnet) for Solving PDEs

主讲人：项阳 教授（香港科技大学）

讲座时间：2023年12月1日10：00-11：00

讲座地点：深圳大学粤海校区汇星楼一楼四号教室

内容概述：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 design 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.

主讲人简介： 项阳教授，香港科技大学数学系教授。2001年博士毕业于纽约大学科朗数学研究所，2001至2003年于普林斯顿大学开展博士后工作，2003年加入香港科技大学数学系。主要研究领域在于材料科学中的数学建模、数值计算以及相应的分析，在与缺陷相关的材料建模与计算上取得了一系列具有重要意义的原创性成果。是美国工业与应用数学协会材料科学中数学问题大会2021年大会报告人，入选2021、2022年斯坦福大学发布的全球Top 2%科学家。现任东亚工业与应用数学会主席。

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