# Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

arXiv: https://arxiv.org/abs/1710.08234 · HTML: https://mlsanity.com/paper/1710.08234/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2017.

## Built on by (most cited first, 9 of 9)

- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)
- [Convergence Rates for Regularized Optimal Transport via Quantization](https://mlsanity.com/paper/2208.14391/) (2022)
- [Genetic column generation: Fast computation of high-dimensional multi-marginal optimal transport problems](https://mlsanity.com/paper/2103.12624/) (2021)
- [Path Structured Multimarginal Schr"odinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Software](https://mlsanity.com/paper/2310.00604/) (2023)
- [Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridge](https://mlsanity.com/paper/2405.12463/) (2024)
- [Neural Estimation for Scaling Entropic Multimarginal Optimal Transport](https://mlsanity.com/paper/2506.00573/) (2025)
- [Sinkhorn Algorithm for Sequentially Composed Optimal Transports](https://mlsanity.com/paper/2412.03120/) (2024)
- [Approximative Algorithms for Multi-Marginal Optimal Transport and Free-Support Wasserstein Barycenters](https://mlsanity.com/paper/2202.00954/) (2022)

## Abstract (arXiv)

Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical method based on Sinkhorn's algorithm for the entropic regularization of optimal transport. We also make a detailed comparison of this entropic regularization with the so-called Bredinger entropic interpolation problem. Numerical results in dimension one and two illustrate the feasibility of the method.