Optimal transport induces a geometrically intuitive metric on the space of probability measures and is a powerful tool for image and data analysis. With the evolution of efficient numerical methods it is becoming increasingly popular. However, in many models the assumption that all measures have unit mass and that mass is exactly preserved locally are too restrictive, for instance in biochemical growth processes. Hence, in recent years, `unbalanced’ transport problems, that allow creation or annihilation of mass during transport, have received increased attention. In this talk we present several formulations for such problems, efficient numerical methods and illustrate applications and advantages of unbalanced metrics.
This is joint work with Lénaïc Chizat, Gabriel Peyré, François-Xavier Vialard and Benedikt Wirth.