Mixed L-2-Wasserstein optimal mapping between prescribed density functions

A time-dependent minimization problem for the computation of a mixed L-2-Wa sserstein distance between two prescribed density functions is introduced i n the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed i nitial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient metho d is used to solve this relaxed problem. We obtain an algorithm which compu tes an interpolated L-2-Wasserstein distance between two densities and the corresponding optimal mapping.