Teaching Spring 2023 Math6540

Course: Computational Optimal Transport

Semester: Spring 2023;

Time: 01/16/2022-04/27/2022, TR 02:20pm-03:35pm;

Location: Philips 730;

Instructor: Yanxiang Zhao, Phillips 709

Phone: 202-994-0606

Email: yxzhao at email dot gwu dot edu

Office Hour: by appointment

Course Description

This course is aimed at advanced graduate students in mathematics, science and engineering. The goal of this course is to provide a broad entry point to Optimal Transport for students with a basic knowledge in linear algebra, differential equations, scientific computing who are seeking to expand their background to include methods in optimization, data science, machine learning.

Prerequisites

Linear Algebra;
Numerical Linear Algebra;
Basic knowledge of convex optimization;
Numerical Analysis (or their equivalents or permission of instructor);
Knowledge of a programing language.

Textbook

Primary textbook: Computational Optimal Transport by G. Peyre and M. Cuturi [link];
Other useful references:
1. Topics in Optimal Transportation by C. Villani;
  - This one is comprehensive textbook on OT from applied analysis viewpoint.
2. Optimal Transport for applied mathematicians, F. Santambrogio, Birkäuser, NY, 2015;
  - This is an easier-to-follow book than Villani's, with some numerical components.
3. An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flow by A. Figalli and F. Glaudo;
  - A short notes, easy to read.
4. Plenty of textbooks and videos available online.

Learning Outcomes

As a result of completing this course, the students will be able to understand:

Definition of OT;
Entropic regularized OT;
Numerical implementation of entropic regularized OT;
Dynamic formulations of OT;
Applications of OT;
Variants of OT.

Average minimum amount of independent, out-of-class, learning expected per week

More than 2/3 of the time you devote to this class should take place outside the classroom (lecture and recitation). Even the best students in the class should plan on spending an average of at least 6 hours a week on homework and other studying. Students who struggle with the material may need to spend more time in order to earn a grade they will find acceptable.

Course Calendar

	Mon	Tue	Wed	Thu	Fri
Week 1	Jan 16	Jan 17	Jan 18	Jan 19	Jan 20
Week 2	Break	Jan 24	Jan 25	Jan 26	Jan 27
Week 3	Jan 30	Jan 31	Feb 01	Feb 02	Feb 03
Week 4	Feb 06	Feb 07	Feb 08	Feb 09	Feb 10
Week 5	Feb 13	Feb 14	Feb 15	Feb 16	Feb 17
Week 6	Feb 20	Feb 21	Feb 22	Feb 23	Feb 24
Week 07	Break	Feb 28	Mar 01	Mar 02	Mar 03
Week 08	Mar 06	Mar 07	Mar 08	Mar 09: Midterm	Mar 10
Week 09	Break	Break	Break	Break	Break
Week 10	Mar 20	Mar 21	Mar 22	Mar 23	Mar 24
Week 11	Mar 27	Mar 28	Mar 29	Mar 30	Mar 31
Week 12	Apr 03	Apr 04	Apr 05	Apr 06	Apr 07
Week 13	Apr 10	Apr 11	Apr 12	Apr 13	Apr 14
Week 14	Apr 17	Apr 18	Apr 19	Apr 20	Apr 21
Week 15	Apr 24	Apr 25	Apr 26	Apr 27: Final	Apr 28
Week 16

Homework

Homework 01;

Homework 02;

Exams

If you have a legitimate conflict with the test dates and times (such as Student-athletes accommodation and Religious holidays), please contact the instructor as soon as possible, do not wait until shortly (within 24 hours) before the test.
If you miss a test because of an illness, you must inform the instructor before the test, and get a note from your doctor in order to be allowed to make the test up at a later date. Unexplained missed tests will not be excused or allowed to be made up.
Assistance of any type (notes in any form, books, calculator, smartphone apps, etc.) is strictly banned during exams. Using the work of others on exams is strictly prohibited.
One in-class midterm exam is scheduled at Feb 24.
Final exam is scheduled at Apr 21.

Grading

Your course grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

	A	A-	B+	B	B-	C+	C	C-	D+	D	D-
Scale	95%	90%	87%	83%	80%	77%	73%	70%	67%	63%	60%

Your cumulative average will be the following weighted average:

	In-class performance	Midterm	Final
Scheme	50%	20%	30%

Class Policies

University policy on Religious Holidays:

Students should notify faculty during the first week of the semester of their intention to be absent from class on their day(s) of religious observance;
Faculty should extend to these students the courtesy of absence without penalty on such occasions, including permision to make up examinations;
Faculty who intend to observe a religious holiday should arrange at the beginning of the semester to reschedule missed classes or to make other provisions for their course-related activities.

Academic Integrity

Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of other without crediting them and without appropriate authorization, and the fabrication of information. For the remainder of the code, see: http://www.gwu.edu/~ntegrity/code.html.

Support for Students Outside the Classroom

Disability Support Services (DSS): Any student who may need an accommodation based on the potential impact of a disability should contact the DSS office at 202-994-8250 in the Rome Hall, Suite 102, to establish eligibility and to coordinate reasonable accommodations. For additional information please refer to: http://gwired.gwu.edu/dss/.
University Counseling Center (UCC): The UCC (202-994-5300) offers 24/7 assistance and referral to address students' personal, social, career, and study skills problems. Services for students include: crisis and emergency mental health consultations; confidential assessment, counseling services (individual and small group), and referrals. For additional information please refer to: http://counselingcenter.gwu.edu/.

Security

In the case of an emergence, if at all possible, the class should shelter in place. If the buliding that the class is in is affected, follow the evacuation procedures for the building. After evacuation, see shelter at a predetermined rendezvous location.

Student Responsibilities and Classroom Courtesy:

You are responsible for knowing about all announcements made in class related to homework assignments, exams etc., and for all material covered in class.
Be aware of the University's Code of Academic Integrity, see http://www.gwu.edu/~ntegrity for details. If cases of academic dishonesty arise, whether on homework assignments, quizzes or exams, they will be pursued to their conclusion.
Each student must conduct him or herself in a manner that promotes a positive atmosphere, conveys mutual respect, and creates no distractions, thereby allowing all students to focus on our goal: learning NUMERICAL ANALYSIS. In particular:
cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- everyone should make a serious effort to arrive promptly for the start of class;
- except for serious reasons, once in class everyone should remain in class until the class is over;
- apart from the lecture, students asking the instructor questions, and students responding to the instructor's questions, the class should be silent.

Questions

Everyone is strongly encouraged to ask questions during class, and during office hours! Should you need further assistance, you may consider hiring a tutor (the department keeps a list of tutors; copies are available outside Phillips Hall 739).