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

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arxiv 2401.11354 v1 pith:C4SAROFP submitted 2024-01-21 math.PR cs.LGstat.ME

Mingtao Xia , Xiangting Li , Qijing Shen , Tom Chou This is my paper · ORCID
classification math.PRcs.LGstat.ME
keywords sdessquaredanalysisdemonstratedifferentialdistancedistance-basedequations
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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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  1. A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks

    cs.LG 2025-07 conditional novelty 5.0 of 10

    A generalized Wasserstein-2 loss with a differentiable surrogate lets stochastic neural networks reconstruct random field models whose outputs combine continuous and categorical variables.

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