An optimal transport problem between two densities can be formulated as a kinetic problem governed by a transport equation relating the time change in density to the negative product of density and velocity field.

“Uh we can frame an optimal transport problem from one density or to another as a ca a kinetic problem, where effectively we follow uh this transport equation, so the uh the the density change over time is equal to the negative of the uh the current density times the velocity field and we we do the uh diverted around it.”