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arXiv · 2401.11354

Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations

Mingtao Xia·Xiangting Li·Qijing Shen·Tom Chou
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Abstract

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.

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BibTeXRIS

Mingtao Xia, Xiangting Li, Qijing Shen, Tom Chou. 2024-01-21. Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations. https://arxiv.org/abs/2401.11354

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