Forward-backward doubly stochastic differential equations (FBDSDEs) are related to a type of quasi-linear parabolic stochastic partial differential equations (SPDEs). We propose a deep learning-based numerical algorithm for solving such equations. Using deep neural networks as approximations of the controls, we can deal with high-dimensional cases. Numerical experiments are carried out to demonstrate the accuracy and efficiency of the proposed numerical algorithm.

中文翻译：

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通过深度学习解决高维前后向双SDE及其相关SPDE

向前-向后双随机微分方程（FBDSDE）与一种准线性抛物线型随机偏微分方程（SPDE）有关。我们提出了一种基于深度学习的数值算法来求解此类方程。使用深度神经网络作为控件的近似值，我们可以处理高维情况。通过数值实验证明了所提算法的准确性和有效性。