Wasserstein Gradient Flow of the Fisher Information from a Non-Smooth Convex Minimization Viewpoint

Guillaume Carlier, Jean David Benamou, Daniel Matthes

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the Derrida-Lebowitz-Speer-Spohn (DLSS) quantum drift diffusion equation, which is the Wasserstein gradient flow of the Fisher information, we study in details solutions of the corresponding implicit Euler scheme. We also take advantage of the convex (but non-smooth) nature of the corresponding variational problem to propose a numerical method based on the Chambolle-Pock primal-dual algorithm.

Original languageEnglish
Pages (from-to)359-378
Number of pages20
JournalJournal of Convex Analysis
Volume31
Issue number2
StatePublished - 2024

Keywords

  • Chambolle-Pock algorithm
  • DLSS equation
  • Fisher information
  • Wasserstein distance
  • convex duality

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