Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations
This work addresses the challenge of SDE reconstruction for applications in fields like finance or physics, but it appears incremental as it builds on existing Wasserstein distance concepts.
The authors tackled the problem of reconstructing stochastic differential equations (SDEs) from noisy data by proposing a squared Wasserstein-2 distance-based loss function, demonstrating its efficiency in numerical experiments across various applications.
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.