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

Mingtao Xia, Xiangting Li, Qijing Shen, Tom Chou
1/21/2024
math.PRcs.LGstat.ME

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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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Cite this paper

@article{xia2024squared,
  title  = {Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations},
  author = {Mingtao Xia and Xiangting Li and Qijing Shen and Tom Chou},
  year   = {2024},
  eprint = {2401.11354},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2401.11354v1}
}

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