nmboffi / sbtm

Repository for score-based transport modeling.

Score-Based Transport Modeling

This repository provides an efficient implementation in jax of the score-based transport modeling algorithm for solving the Fokker-Planck equation in high dimension. This method may also find applications in flow-based solutions of other high-dimensional partial differential equations using machine learning.

Above is a beautiful phase portrait for a two-dimensional active swimmer produced with the algorithm.

Installation

The implementation is built on Google's jax package for accelerated linear algebra and DeepMind's haiku package for neural networks. Both can be installed by following the guidelines at the linked repositories.

Usage

Experiments from the paper can be reproduced by running the files contained in the experiments directory.

The main implementation of the algorithm can be found in sbtm_sequential.py, while analysis routines used for the results in the publication can be found in sbtm_analysis.py.

Other systems can be implemented by adding the needed dynamics to drifts.py.

Referencing

If you found this repository useful, please consider citing

[1] N. M. Boffi and Eric Vanden-Eijnden. “Probability flow solution of the Fokker-Planck equation,” Machine Learning: Science and Technology (2023).

@misc{boffi2023probability,
      title={Probability flow solution of the Fokker-Planck equation}, 
      author={Nicholas M. Boffi and Eric Vanden-Eijnden},
      year={2023},
      eprint={2206.04642},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}