A Computational Framework for Solving Wasserstein Lagrangian Flows

Explore a comprehensive lecture on a computational framework for solving Wasserstein Lagrangian flows. Delve into the dynamical formulation of optimal transport, examining various choices of underlying geometry and density path regularization. Learn how these combinations yield different variational problems, encompassing variations of optimal transport such as the Schrödinger bridge and unbalanced optimal transport. Discover a novel deep learning-based framework that approaches these problems from a unified perspective, without requiring simulation or backpropagation through learned dynamics trajectories. Examine the framework's versatility through its application to single-cell trajectory inference, demonstrating the importance of incorporating prior knowledge into dynamics for accurate predictions. Follow along as the speaker covers Lagrangian mechanics, Wasserstein Lagrangian mechanics, optimal transport, Schrödinger bridge, the computational framework, applications, results, and concludes with a Q&A session.

- Intro + Motivation
- Lagrangian Mechanics
- Wasserstein Lagrangian Mechanics
- Optimal Transport
- Schrödinger Bridge
- Computational Framework
Applications + Results
- Q&A