MA595, Computational Optimal Transport and Deep Generative Models

Course Information:


Optimal Transport has gained significant attention in recent years across a range of applications, particularly in machine learning and deep learning. This course explores the computational aspects of optimal transport and its variants. Topics will include the theoretical foundation of optimal transport and the Wasserstein distance, along with numerical algorithms such as linear programming, duality formulations, and Sinkhorn’s algorithm. A key focus will be on the dynamic formulation of optimal transport and variational PDE-based algorithms. Additionally, the course will delve into connections between optimal transport and various deep generative models, including Generative Adversarial Networks (GANs), normalizing flows, diffusion models et al. By the end of the course, students will have a deep understanding of both the theory and practical algorithms for optimal transport, as well as how these methods integrate with modern deep learning models.