Course Syllabus

Math 680J   Optimal Transport and Deep Learning 

Fall 2021@ISU   

I am excited to have you in my class this Spring.  Through this semester  we will  introduce  basic tools from the optimal transport theory,  deep neural networks  and their training,  as well as a selected set of research topics in deep learning.

Regarding to the pandemic we are in, we want to do everything we can to protect you, your classmates, your professors/TAs, and your family members -- everyone really-- from possible infection. This is why we ask that you follow the guidelines laid out by ISU  at  ISU Covid-19  Information be responsible for abiding by the university’s COVID-19 health and safety expectations.  

Here below is the course info: 

  • Instructor:  Hailiang Liu
  • Course Schedule
    Jan 25: course opens
    TR 11:00A -- 12:15P,  Virtually via Zoom.
    May 06: course ends 

  • Course content and references: 
    The material will be based on lecture notes and a collection of book chapters.  

    Part I:   Introduction to Optimal Transport   
    [1] F. Santambrogio. 
    Optimal transport for applied Mathematicians. Vol. 87, Progress in Nonlinear Differential Equations and Their Applications, Birkhaueser, 2015.

    Part II: Introduction to Deep Learning 
    [1] Ian Goodfellow and Yoshua Bengio and Aaron Courville.
    Deep Learning. MIT Press, 2016;

  • Topics   We plan to have 25 regular lectures. Plus one review and two project presentations.

    Part I Introduction to optimal transport theory [10 lectures, week 1~6] 
    1. Primal and dual problems
    2. Minimal flows and transport density
    3. Wasserstein spaces
    4. Numerical methods
    5. Gradient flows

    Part II: Introduction to Deep Learning [16 lectures, week 6~14]  

    1. Mathematics and machine learning basics 
    2. Deep neural networks and training 
    3. Deep learning research 

  • To see further course information, course plan by topics, and course plan by weeks,  
    please click the following button 

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