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.

翻译：我们分析了与两个随机微分方程相关的两个概率分布之间的平方Wasserstein-2距离，并基于该分析提出在含噪声数据的随机微分方程重构中使用平方距离损失函数。为验证基于Wasserstein距离损失函数的实用性，我们通过数值实验展示了该方法在重构多个应用场景中随机微分方程的高效性。