Project webpage: https://www.gpeyre.com/ot4ml
Project homepage · PDE4ML survey · Interactive book · Rendered figure gallery · Resources · GitHub source
This repository gathers the OT4ML book, the PDE4ML survey, the executable notebooks used to reproduce the figures, a shorter set of teaching notebooks, and an experimental MyST web prototype.
PDEs for Machine Learning is a long survey of PDE tools for machine learning, written with an optimal-transport bias. It reorganizes the OT4ML material most relevant to dynamic optimal transport, Wasserstein gradient flows, particle limits, diffusion models, flow matching, mean-field training, and transportation views of modern architectures.
Sources and build notes live in PDE4ML/.
The book Optimal Transport for Machine Learners is available on arXiv.
The book figures are generated from executable notebooks and assembled by the
LaTeX source. The current searchable gallery has been checked against the live
LaTeX and MyST figure references: it exposes 129 figure views, covers all 129
referenced OT4ML/figures/<figure-name>/ directories, and every active view has
a notebook link, thumbnail, and generated PDF panels. The manuscript contains
132 LaTeX figure labels because some figure directories generate several labeled
figures. Browse the rendered web gallery at
www.gpeyre.com/ot4ml/notebooks-figures/index.html
or the Markdown version in
notebooks-figures/README.md, with thumbnails,
notebook links, and Open in Colab badges. The figure notebooks are
self-bootstrapping on Colab: they load one lightweight shared core, fetch only
explicit computational assets, and install only missing dependencies such as
POT. They neither clone the repository nor add it wholesale to Python's import
path.
Each live figure notebook writes PDF panels to OT4ML/figures/<figure-name>/,
where the LaTeX source assembles them into the book. Retired exploratory
notebooks live in notebooks-figures/removed/ and are not part of the paper
gallery.
The course notebooks below are compact, self-contained introductions to the main computational ideas. Helper functions are documented, code cells stay short enough to inspect, and the heavier demos use modest default budgets so they remain practical in Colab. Each one can be opened locally or launched in Colab.
An experimental MyST/Jupyter Book 2 prototype lives in
myst/. It mirrors the LaTeX book front matter, 15 main chapters,
conclusion, notation table, and index while fusing the book text
with executable figures and browser-native interactive demos. The rendered static version is available from the
project homepage. The local
workflow, the static-site build, and the offline behavior of the interactive demos
are documented in myst/README.md.
- Monge and Kantorovich: interactive slides, SpeakerDeck
- Entropic Regularization: interactive slides, SpeakerDeck
- Dual and Semidiscrete: interactive slides, SpeakerDeck
- Gradient Flow and Diffusion Models: interactive slides, SpeakerDeck
A rendered resource portal is available at www.gpeyre.com/ot4ml/resources.html.
Core books and monographs cited in the book:
- Mass Transportation Problems, Vol. I: Theory, Svetlozar T. Rachev & Ludger Rüschendorf, Springer, 1998.
- Mass Transportation Problems, Vol. II: Applications, Svetlozar T. Rachev & Ludger Rüschendorf, Springer, 1998.
- Topics in Optimal Transportation, Cédric Villani, AMS, 2003.
- Optimal Transport: Old and New, Cédric Villani, Springer, 2009.
- Optimal Transport for Applied Mathematicians, Filippo Santambrogio, Birkhäuser, 2015.
- Gradient Flows in Metric Spaces and in the Space of Probability Measures, Luigi Ambrosio, Nicola Gigli & Giuseppe Savaré, Springer, 2006.
- Optimal Transport Methods in Economics, Alfred Galichon, Princeton University Press, 2016.
- Statistical Optimal Transport, Sinho Chewi, Jonathan Niles-Weed & Philippe Rigollet, 2024.
Computational references and long reviews cited in the book:
- Computational Optimal Transport, Gabriel Peyré & Marco Cuturi, Foundations and Trends in Machine Learning, 2019.
- A User's Guide to Optimal Transport, Luigi Ambrosio & Nicola Gigli, Lecture Notes in Mathematics, 2013.
- A Survey of the Schrödinger Problem and Some of Its Connections with Optimal Transport, Christian Léonard, Discrete and Continuous Dynamical Systems, 2014.
- A Review of Matrix Scaling and Sinkhorn's Normal Form for Matrices and Positive Maps, Martin Idel, 2016.
- Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey, Abdelwahed Khamis, Russell Tsuchida, Mohamed Tarek, Vivien Rolland & Lars Petersson, IEEE TPAMI, 2024.
- Recent Advances in Optimal Transport for Machine Learning, Eduardo F. Montesuma, Fred Ngolè Mboula & Antoine Souloumiac, 2023.
- A Survey of Optimal Transport for Computer Graphics and Computer Vision, Nicolas Bonneel & Julie Digne, Computer Graphics Forum, 2023.
Most figures in the book are generated with standard Python scientific tools, with several OT computations relying on POT, the Python Optimal Transport library cited and acknowledged in the manuscript.