Multi-marginal interacting kinetic Schrödinger bridges

Extend the interacting kinetic Schrödinger bridge framework from endpoint constraints to time-resolved distributions through a multi-marginal formulation, enabling inference from time series of population snapshots.

Background

The paper constrains the swarm distribution at only the initial and terminal times, considering either full phase-space distributions or spatial marginals. In applications such as developmental trajectory inference, observations may instead consist of population snapshots over multiple times. The authors explicitly identify extending the framework to incorporate such time-resolved distributions as another research direction.