Foundations and Applications of AI

Organizer

包承龙

Speakers

15:00-16:00

Ling Guo 郭玲

上海师范大学数学系教授

16:00-17:00

Liang Yan 闫亮

东南大学教授

Time

Friday, 15:00 - 17:00

Apr. 18, 2025

Venue

C548, Shuangqing Complex Building

15:00 - 16:00

Uncertainty Quantification in Scientific Machine Learning via Information Bottleneck

Neural networks (NNs) are revolutionizing computational paradigms in physics and engineering by offering novel ways to integrate data with mathematical laws. This transformative approach enables the solution of challenging inverse and ill-posed problems that remain intractable for traditional methods. However, quantifying errors and uncertainties in NN-based inference presents unique complexities compared to conventional techniques. In this talk, we introduce a new framework for uncertainty quantification based on the information bottleneck principle (IB-UQ), designed for scientific machine learning tasks such as deep neural regression and neural operator learning. Additionally, we will present a physics-informed extension of IB-UQ for PDE-related problems. The capability of the proposed IB-UQ framework is demonstrated with several numerical examples.

报告人简介：郭玲，上海师范大学数学系教授, 博士生导师。2007年毕业于上海交通大学数学科学学院后进入上海师范大学工作，美国布朗大学和普渡大学数学系访问学者。主要研究领域为不确定性量化、概率科学计算和深度学习，在应用数学综合权威期刊以及计算数学领域权威期刊发表多篇学术论文，主持承担多项国家级与省部级科研项目。

16:00 - 17:00

基于深度学习的偏微分方程反问题求解及其应用

近年来，基于深度学习和微分方程（PDE）结合的科学机器学习（SciML）方法逐渐成为科学计算领域研究的热点，在科学探究和工程应用的诸多领域得到广泛应用。本报告中，我们在回顾深度学习求解偏微分方程反问题的几种常用框架的基础上，介绍我们在该领域所设计的几种方法，包括自适应算子学习、基于失效信息的PINNs方法以及针对反障碍散射所设计的SRnet框架等。

报告人简介：闫亮，东南大学教授、博士生导师。主要从事主要从事不确定性量化、贝叶斯建模与计算、反问题以及科学机器学习的研究。先后主持包括国家自然科学基金重大研究计划培育项目在内的多项课题,在《SIAM J. Sci. Comput.》《Inverse Problems》《J. Comput. Phys.》等国内外刊物上发表40多篇学术论文.