| Abstract: |
| In the study of multi-particle dynamics and mean-field equations, the Wasserstein distance plays a central role in quantifying the evolution of particle distributions. With Likhit Ganedi (University of Utah), we introduce a simple algorithm for the computation of the Wasserstein metric based on a gradient ascent flow for the Monge-Kantorovich dual formulation, and using a discrete approximation of the double c-transform. The method is computationally efficient and does not require entropic regularization, which can otherwise introduce approximation errors.
In addition, we develop a framework for analyzing its global convergence by studying the discrete-to-continuous limit of the underlying dynamics. This approach yields convergence guarantees and highlights a connection with elliptic regularity. |
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