Squared Wasserstein-2 Distance for Efficient Reconstruction of
  Stochastic Differential Equations
Mingtao Xia Xiangting Li Qijing Shen Tom Chou
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.