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[2602.22003] Neural solver for Wasserstein Geodesics and optimal transport dynamics
Summary
This article presents a novel neural solver for computing Wasserstein geodesics and optimal transport dynamics, enhancing the modeling of distributional relationships in machine learning.
Why It Matters
The introduction of a sample-based neural solver addresses a significant challenge in optimal transport theory, providing a flexible framework that can be applied to various cost functions. This advancement has implications for fields such as machine learning, data science, and optimization, where understanding distributional relationships is crucial.
Key Takeaways
- Introduces a neural solver for Wasserstein geodesics using deep learning.
- Recasts the optimal transport problem as a minimax optimization task.
- Demonstrates flexibility in extending the framework to general cost functions.
- Provides effective solutions for both synthetic and real datasets.
- Enables direct sampling from target distributions through the estimated OT map.
Computer Science > Machine Learning arXiv:2602.22003 (cs) [Submitted on 25 Feb 2026] Title:Neural solver for Wasserstein Geodesics and optimal transport dynamics Authors:Hailiang Liu, Yan-Han Chen View a PDF of the paper titled Neural solver for Wasserstein Geodesics and optimal transport dynamics, by Hailiang Liu and 1 other authors View PDF HTML (experimental) Abstract:In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein geodesic between a source and target distribution, along with the associated velocity field. Building on the dynamical formulation of the optimal transport (OT) problem, we recast the constrained optimization as a minimax problem, using deep neural networks to approximate the relevant functions. This approach not only provides the Wasserstein geodesic but also recovers the OT map, enabling direct sampling from the target distribution. By estimating the OT map, we obtain velocity estimates along particle trajectories, which in turn allow us to learn the full velocity field. The framework is flexible and readily extends to general cost functions, including the commonly used quadratic cost. We demonstrate the effectiveness of our method through experiments on both synthetic and real datasets. Comments: Subjects: Machine Learning (cs.LG); Optimization and Control (math.OC); ...
