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

Mingtao Xia, Xiangting Li, Qijing Shen, Tom Chou

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: Neural Stochastic Differential Equation, Wasserstein distance, Uncertainty Quantification, Inverse problem

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TL;DR: We prove bounds for the squared Wasserstein distance between probability measures for two stochastic differential equations (SDEs), based on which we propose an efficient Wasserstein distance loss function for reconstructing SDEs.

Abstract:

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 a
novel squared $W_2$ distance-based loss function for efficiently
reconstructing SDEs from noisy data. To demonstrate the utility of
using our Wasserstein distance-based loss function, we carry out
numerical experiments that show its efficiency in reconstructing SDEs.

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Submission Number: 276