Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917572044128256 |
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| author | Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom |
| author_facet | Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom |
| contents | We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$ distance-based loss functions in the \textit{reconstruction} of SDEs from noisy data. To demonstrate the practicality of our Wasserstein distance-based loss functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that arise across a number of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom Probability Machine Learning Methodology 60H10, 49Q22 We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$ distance-based loss functions in the \textit{reconstruction} of SDEs from noisy data. To demonstrate the practicality of our Wasserstein distance-based loss functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that arise across a number of applications. |
| title | Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations |
| topic | Probability Machine Learning Methodology 60H10, 49Q22 |
| url | https://arxiv.org/abs/2401.11354 |