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arXiv · 1809.07083

Dynamical Optimal Transport on Discrete Surfaces

Hugo Lavenant·Sebastian Claici·Edward Chien·Justin Solomon
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Abstract

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation of quadratic optimal transport proposed for flat domains by Benamou and Brenier [2000], adapted to discrete surfaces. Our structure-preserving construction yields a Riemannian metric on the (finite-dimensional) space of probability distributions on a discrete surface, which translates the so-called Otto calculus to discrete language. From a practical perspective, our technique provides a smooth interpolation between distributions on discrete surfaces with less diffusion than state-of-the-art algorithms involving entropic regularization. Beyond interpolation, we show how our discrete notion of optimal transport extends to other tasks, such as distribution-valued Dirichlet problems and time integration of gradient flows.

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BibTeXRIS

Hugo Lavenant, Sebastian Claici, Edward Chien, Justin Solomon. 2018-09-19. Dynamical Optimal Transport on Discrete Surfaces. https://doi.org/10.1145/3272127.3275064

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