Mathematical Sciences Department
Colloquium
Speaker: Qiao Zhuang, WPI
Friday, January 12th
11:00 am - 12:00 pm
Salisbury Labs 104
Zoom Meeting ID: 938 8407 5985
Title: Scientific Machine Learning Interacts and Synergizes with Traditional Numerical Methods
Abstract: In this talk, we will explore the dynamic interface between scientific machine learning (SciML) and traditional numerical methods. As computational challenges in science and engineering continue to become more intricate, the need for innovative solutions becomes imperative. SciML emerges as a transformative approach, integrating machine learning techniques with scientific principles and data. SciML forms a synergistic interplay with traditional numerical methods, leading to enhanced capabilities in tackling complex problems in various scientific fields.
The presentation focuses on two main topics. Firstly, we delve into a two-scale neural network method for partial differential equations with small parameters. We propose a concise approach to address the large gradients or high-frequency issues posed by the small parameters, without adding complexity to loss functions or training processes of neural networks. Secondly, we investigate a class of finite element methods that can solve interface problems on interface-independent meshes. Finally, we discuss the interplay and mutual enhancement between neural network approaches and finite element methods, with a particular focus on their applications to interface problems.