Forward-Euler time-discretization for Wasserstein gradient flows can be wrong
<|reference_start|>Forward-Euler time-discretization for Wasserstein gradient flows can be wrong: 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 even for a simple case where the energy functional is defined as the KL divergence against some nicely structured probability densities. A simple explanation of this failure is also discussed.<|reference_end|>
@article{xu2024forward-euler,
    title={Forward-Euler time-discretization for Wasserstein gradient flows can be
  wrong},
    author={Yewei Xu, Qin Li},
    journal={arXiv preprint arXiv:2406.08209},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.08209},
    primaryClass={stat.ML cs.LG math.OC}
}