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

• URL: http://arxiv.org/abs/2401.11354v1
• Date: Sun, 21 Jan 2024 00:54:50 GMT
• Title: Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations
• Authors: Mingtao Xia and Xiangting Li and Qijing Shen and Tom Chou
• Abstract summary: We provide an analysis of the squared $W$ distance between two probability distributions associated with Wasserstein differential equations (SDEs) Based on this analysis, we propose the use of a squared $W$ distance-based loss functions in the textitreconstruction of SDEs from noisy data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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