3 papers
stat.ML2026
Random Coordinate Descent on the Wasserstein Space of Probability Measures
Yewei Xu, Qin Li
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional meth…
math.NA2025
Forward Euler for Wasserstein Gradient Flows: Breakdown and Regularization
Yewei Xu, Qin Li
Wasserstein gradient flows have become a central tool for optimization problems over probability measures. A natural numerical approach is forward-Euler time discretization. We sho…
stat.ML2024
Forward-Euler time-discretization for Wasserstein gradient flows can be wrong
Yewei Xu, Qin Li
In this note, we examine the forward-Euler discretization for simulating Wasserstein gradient flows. We provide two counter-examples showcasing the failure of this discretization e…