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

2024/01/21 by Mingtao Xia, Xia, Mingtao, Xiangting Li +5 · 1 citation
Computer Science · Mathematics · #49Q22 #60H10 #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2401.11354

openalex publication_date 2024/01/21 · openalex created_date 2024/01/24 · openalex updated_date 2026/07/28

Abstract

We provide an analysis of the squared Wasserstein-2 (W₂) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared W₂ distance-based loss functions in the 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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