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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08209 |
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| _version_ | 1866911914377871360 |
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| author | Xu, Yewei Li, Qin |
| author_facet | Xu, Yewei Li, Qin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forward-Euler time-discretization for Wasserstein gradient flows can be wrong Xu, Yewei Li, Qin Machine Learning Optimization and Control 65M12 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. |
| title | Forward-Euler time-discretization for Wasserstein gradient flows can be wrong |
| topic | Machine Learning Optimization and Control 65M12 |
| url | https://arxiv.org/abs/2406.08209 |