Fractional weak adversarial networks for the stationary fractional advection dispersion equations. (English) Zbl 07920854
Summary: In this article, we propose the fractional weak adversarial networks (f-WANs) for the stationary fractional advection dispersion equations 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 34A08 | Fractional ordinary differential equations |
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