Lecture 1. An Introduction to GMG and AMG
Speaker: Ludmil Zikatanov, Penn State University
Multigrid methods (MGs) is a name used for a suite of advanced techniques for the solution of linear systems. We will introduce the basic components of geometric multigrid methods (GMGs) and algebraic multigrid methods (AMGs) such as smoothing via iterative methods, coarsening using adjacency graphs and the combination of these tools which give rise to several well known methods. We will also present some of the adaptive AMG techniques which construct iteratively better and better coarse spaces.
Instructor: Prof. Ludmil Zikatanov
Lecture 2. Introduction to Convolutional Neural Networks
Speaker: Zhanxing Zhu, Peking University
In this short tutorial, I will provide a comprehensive introduction to the convolutional neural networks (CNNs). CNNs are the most successful deep learning architectures and have been wildly used in many AI tasks and scientific domains. I will introduce (1) the basic components of CNNs, (2) popular architectures, including LeNet, AlexNet, ResNet, etc, (3) applications of CNNs in various tasks, (4) visualization of CNNs, (5) instability of CNN and (6) some regularization strategies. The tutorial requires some basic mathematical background and assumes no prior knowledge of machine learning or deep learning.
Instructor: Prof. Zhanxing Zhu
Teaching assistants: TBA
Lecture 3. An Integrated Introduction to Multigrid and Deep Learning
Speaker: Jinchao Xu, Penn State University
In this short course, an integrated introduction will be given to both multigrid methods and machine learning based on deep neural networks. The presentation will be elementary as it assumes little prior knowledge on both subjects and yet advanced as it will quickly reach to core issues in the relevant algorithm/model formulation, mathematical understanding and practical applications. Practice problems will be given to both theoretical analysis and practical applications that uses iFEM (for multigrid) and TensorFlow or Pytorch (for Deep Learning).
Instructor: Prof. Jinchao Xu
Teaching assistants: Juncai He and Xiaodong Jia (Peking University)