Numerical methods for (unbalanced) optimal transport

This code is not maintained anymore and written in a deprecated version of Julia. For an stable implementation of unbalanced optimal transport, see Gabriel Peyré's code.

This Julia toolbox provides several tools for solving optimal transport, the unbalanced extensions and related problems.

What you can find here:

• a computation of (unbalanced) optimal transport geodesics through extensions of the Benamou-Brenier dynamic formulation.
• a demonstration of "scaling algorithms" for computing (unbalanced) optimal transport using the Kantorovich formulation
• color transfer using optimal transport ;
• Wasserstein gradient flow of the total variation functional (in 1d)
• a tumor growth model computed as a gradient flow with an unbalanced optimal transport metric.
• (in construction) (unabalanced) OT barycenters for big problems (using multiscale).

Check the associated article where the mathematical framework and algorithms are described:

• An interpolating distance between optimal transport and Fisher-Rao
• Unbalanced optimal transport: geometry and Kantorovich formulation
• Scaling algorithms for unbalanced optimal transport
• in preparation(with S. Di Marino) : a tumor growth Hele-Shaw problem as a gradient flow

and see the associated notebooks for a simple overview.

Extensions in preparation (if time permits!):

• extension of the dynamic solver to Riemannian manifolds
• gradient flow of the total variation in 2D