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

arXiv: https://arxiv.org/abs/2401.11354 · HTML: https://mlsanity.com/paper/2401.11354/

## 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 (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Differentiable Ranks and Sorting using Optimal Transport](https://mlsanity.com/paper/1905.11885/) (2019)
- [Sliced Wasserstein Distance for Learning Gaussian Mixture Models](https://mlsanity.com/paper/1711.05376/) (2017)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Orthogonal Estimation of Wasserstein Distances](https://mlsanity.com/paper/1903.03784/) (2019)
- [Fast and Smooth Interpolation on Wasserstein Space](https://mlsanity.com/paper/2010.12101/) (2020)
- [Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations](https://mlsanity.com/paper/2104.12384/) (2021)
- [Kernel Wasserstein Distance](https://mlsanity.com/paper/1905.09314/) (2019)

## Built on by (most cited first, 3 of 3)

- [An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks](https://mlsanity.com/paper/2406.01653/) (2024)
- [A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty](https://mlsanity.com/paper/2406.06825/) (2024)
- [A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks](https://mlsanity.com/paper/2507.05143/) (2025)

## 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.