Milstein-driven neural stochastic differential equation model with uncertainty estimates

Abstract

Incorporating uncertainty quantification into the modeling of deep learning-based model has become a research focus in the deep learning community. Within this group of methods, stochastic differential equation (SDE)-based models have demonstrated advantages in their ability to model uncertainty quantification. However, the use of Euler’s method in these models introduces imprecise numerical solutions, which limits the accuracy of SDE systems and weakens the performance of the network. In this study, we build a more precise Milstein-driven SDE network (MDSDE-Net) to improve the network performance. In addition, we analyze the convergence of the Milstein scheme and theoretically guarantee the feasibility of MDSDE-Net. Experimental and theoretical results show that the MDSDE-Net outperforms existing models.