A new optimal transport distance on the space of finite Radon measures
By Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov. Advances in Differential Equations, 2015
196 citations recorded by the source corpus.
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula. We establish various topological and geometrical properties of the resulting metric space, derive some formal Riemannian structure, and develop differential calculus following F. Otto's approach. Finally, we apply these ideas to identify an ideal free distribution model of population dynamics as a gradient flow and obtain new long-time convergence results.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/7a7c849639e40f723c65ec98aacf746f9706fdad
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In Applied Mathematics
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- Bernhard Schmitzer
- Filippo Santambrogio
- François-Xavier Vialard
- Soheil Feizi
- Yogesh Kumar Balaji
- Ramalingam Chellappa
Citations in the corpus
- Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation (2020, background): “Two popular ones include entropy regularization [8, 3] and marginal relaxation [13, 6, 7, 9, 12].”
- {Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, background): “This very interesting distance has been independently introduced by three different groups around the year 2015, and we refer to [31,32,60,63,64] for the different presentations and the different considerations which have been investigated so far.”
- Gradient flows and Evolution Variational Inequalities in metric spaces. I: Structural properties (2018, unknown): “(P2(X), dW ), where X is an RCD(K,∞) metric-measure space and φ is the relative entropy functional [88, 69], and there is an intensive research to construct EVI gradient flows in ad-hoc geometric settings for reaction-diffusion equations [54, 25, 57, 55] and systems [65, 48, 56], nonlinear viscoelas”
- Unbalanced optimal transport: Dynamic and Kantorovich formulations (2015, background): “A new metric between measures of non equal masses has recently and independently been proposed by [7, 15].”