In this article, we propose the fractional weak adversarial networks (f-WANs) for the stationary fractional advection dispersion equations (FADE) based on their weak formulas. This enables us to handle less regular solutions for the fractional equations. To handle the non-local property of the fractional derivatives, convolutional layers and special loss functions are introduced in this neural network. Numerical experiments for both smooth and less regular solutions show the validity of f-WANs.

翻译：本文基于稳态分数阶对流弥散方程（FADE）的弱形式，提出了分数阶弱对抗网络（f-WANs）。该方法能够处理分数阶方程中较不光滑的解。为应对分数阶导数的非局部特性，我们在神经网络中引入了卷积层与特殊损失函数。针对光滑解与非光滑解的数值实验均验证了f-WANs的有效性。