mlsanityData to 14 Oct 2026

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

arXiv 2401.11354 ↗First posted 21 Jan 2024math.PR cs.LG stat.MEcited by 3

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Abstract (arXiv)

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 textitreconstruction 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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 18 of its 40 references that are in the map. First posted on arXiv 21 Jan 2024.

Builds on

18 of 40 references.

References · 18

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  10. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
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6 more
  1. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  2. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 45
  3. 2019Orthogonal Estimation of Wasserstein Distancescited by 32
  4. 2020Fast and Smooth Interpolation on Wasserstein Spacecited by 22
  5. 2021Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equationscited by 8
  6. 2019Kernel Wasserstein Distancecited by 4

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Cited by year

Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networkscited by 5
  2. 2024A local squared Wasserstein-2 method for efficient reconstruction of models with uncertaintycited by 2
  3. 2025A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networkscited by 0