3 papers
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…
math.NT2022
Singular Vectors in Real Affine Subspaces
Shreyasi Datta, Yewei Xu
We prove inheritance of measure zero property of the set of singular vectors for affine subspaces and submanifolds inside those affine subspaces. We define a notion of -singular…