Roadmap

What we are working on. Nothing on this page is available yet: names and interfaces may still change.

Ground metrics

Periodic metrics, beyond Ground Metrics: the CUDA solve with rotations and symmetries or an image that is not a constant, 1D ( the circle ).
Partial transport, beyond Ground Metrics: a source heavier than the target, the penalized variant ( a sink of fixed weight ), 3D, gaussian targets, an image on the card, the card's own linear solver for the bordered system.
Radial kernels: costs built from radial functions of $∥ x - y ∥$ , e.g. polynomials, piecewise functions... Beyond RadialExp ( Fokker-Planck ): 3D, the card, other densities than constant pieces, with a periodicity or a sink.

Aggregates with a periodicity: duplicates and close seeds in a periodic domain.
The frame of a target through a periodicity or in partial transport, and the nodes of a mesh.

PolynomialCells: piecewise polynomial densities on a polyhedral cell decomposition, the most general target.

Anisotropic tents on the card, with with_gradient, and in 3D from 2D projections ( Projected Sources ).

Derivatives of the measures, the cells travelling again in the backward pass.
The boxes made by the ranks: the seeds redistributed by exchanges instead of on the host, any number of seeds and of ranks.
More than the measures: moments, the transport itself ( a distributed Newton ), 3D, densities split like the boxes.
Out of core: more boxes than ranks, the boxes that do not fit kept in host memory or on disk ( dask or zarr arrays as inputs ).
Speed: loom.route and loom.scatter_add in parallel, irregular exchanges on GPUs, runs on several GPUs and nodes.

Crowd motion: congested crowds as a Wasserstein gradient flow.
Incompressible Euler: geodesics in the space of measure-preserving maps ( Gallouët-Mérigot scheme ).
Fokker-Planck: Wasserstein gradient flow of entropy plus potential energy.