monge-constrained-flow

This is the official repository for the paper Learning Monge maps with constrained drifting models.

Authors: Théo Dumont

Contact: [email protected]

Dependencies

• numpy
• pytorch
• matplotlib

Reproducing the results of the article

After installing the required dependencies, one has to run main.py (e.g. from terminal). This will store three .npy arrays in the repository and produce a figure afterward.

It runs the implicit and explicit constrained flows as described in the article, along with the Euclidean gradient flow in the space of parameter has a benchmark.

Beware that running the code can take some time (few dozen of minutes on a laptop).

Organization and comments

• main.py is the main file. It relies on the function expe() implemented utils_benchmark.py, calling it with a series of hyper-parameters.
• explicitConstrainedFlow.py (resp. implicitConstrainedFlow.py) implement the explicit (resp. implicit) drifting scheme we introduce in the referenced paper. Similarly, oneshotFlow.py refers to the Euclidean gradient flow.
• mongeMap.py implements our parametrization of Monge Maps as gradients of ICNN.
• dynamics.py implement the Langevin dynamic, giving access to Euclidean and Wasserstein gradient of the functionals.
• sampling.py, MMD.py, Sinkhorn.py are utilitary files.

Comment: This code provides a minimal working example to reproduce the results proposed in our paper. On demand, we can provide a (messier) repository with more options availables (other architectures for Monge maps, other dynamics, other samplers, etc.).