Physics Colloquium: Statistical Physics of Optimal Transport and Schrödinger Bridges

Zoom: https://tau-ac-il.zoom.us/j/84097289852?pwd=bj3ZxsNaOBpvlemc35waxxSLLZ541f.1

Abstract: 

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in many various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between probability distributions.

The `a priori' unrelated Schrödinger bridge problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable path in probability space.

Event Organizer: Dr. Tobias Holder