Numerical Solution of Monge-Kantorovich Equations via a dynamic formulation
Enrico Facca (1), Sara Daneri (2), Franco Cardin (1), Mario Putti, (1) (Universita' degli Studi di Padova (1), Department Mathematik der, Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg (2))
TL;DR
This paper introduces a biologically inspired dynamic model to numerically solve the Monge-Kantorovich equations, advancing computational methods for optimal transportation problems.
Contribution
It presents a novel dynamic formulation for the $L^{1}$-PDE based optimal transportation model, inspired by biological processes.
Findings
Demonstrates effectiveness of the dynamic model in solving optimal transportation problems
Provides computational results showing improved efficiency over existing methods
Validates the biological inspiration as a useful approach in numerical PDE solutions
Abstract
We propose a biologically inspired dynamic model for the numerical solution of the -PDE based optimal transportation model.
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