Оптимальный транспорт и его приложения

2026/2027

Статус: Маго-лего

Кто читает: Департамент анализа данных и искусственного интеллекта

Где читается: Факультет компьютерных наук

Охват аудитории: для своего кампуса

Преподаватели: Пари Кентан Поль Бернар

Язык: русский

Кредиты: 3

Контактные часы: 40

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Аннотация

This course introduces students to the fundamental concepts of optimal transport theory and its wide range of applications in various fields such as economics, machine learning, image processing, and statistics. Through a combination of theoretical lectures and practical exercises, participants will gain both conceptual understanding and hands-on experience with this powerful mathematical framework.

Цель освоения дисциплины

The course aims at presenting the basic results in the field of Optimal Transport

Планируемые результаты обучения

Known about the Monge and Kantorovich formulations of the Optimal Transport problem
Understand general conditions under which an optimal transport plan exists
Be familiar with Kantorovich-Wasserstein distances and their main properties
Know about conditions under which an optimal transport map exists and learn about their particular structure (Brenier Theorem)
Understand the connection between the OT problem and a particular partial differential equation known as the Continuity Equation
Know about the formal Riemannian structure that can be put on the 2-Kantorovich-Wasserstein space