bfm-fast-diffusion

Description

Codes for solving the following problem:

$$ \rho^{n+1} = \text{arg}\min_{\rho} \int \rho \log \rho dx + V(\rho) + \frac{1}{2\tau} W^2_2(\rho, \rho^n) $$

using the back-and-forth method (BFM).

Details of the algorithm can be found in this paper: The back-and-forth method for Wasserstein gradient flows, Matt Jacobs, Wonjun Lee, and Flavien Léger.

The official code website: https://wasserstein-gradient-flows.netlify.app

Installation

Required: Pybind11 package.

Run the following line to install pybind11.

Anaconda:

conda install -c conda-forge pybind11

Pip:

pip install pybind11

Data generation

required parameters

Potential function (-p), number of samples (-ns), mesh grid (-nx), time step size (-dt), num of steps (-nt), GRF parameters (-alp, -tau).

for example

python data_generation.py -p gaussian -ns 2 -nx 64 -nt 10 -dt 0.0005 -alp 4 -tau 10