From Snapshots to Dynamics: An Optimal Transport Approach

Many modern datasets capture populations only at isolated time points, leaving us with snapshots rather than continuous trajectories. How can we reconstruct the underlying dynamics from such partial views? In this talk, I will present a series of projects that use entropic optimal transport (EOT) as a framework for connecting snapshots into dynamic flows. EOT provides a principled way to interpolate between distributions, supporting both the study of density evolution and the design of trajectory inference methods. These results highlight new possibilities for dynamic data analysis and suggest broad directions at the interface of probability, computation, and data science.