  Data-driven discovery of partial differential equations (PDEs) from observed
data in machine learning has been developed by embedding the discovery problem.
Recently, the discovery of traditional ODEs dynamics using linear multistep
methods in deep learning have been discussed in [Racheal and Du, SIAM J. Numer.
Anal. 59 (2021) 429-455; Du et al. arXiv:2103.11488]. We extend this framework
to the data-driven discovery of the time-fractional PDEs, which can effectively
characterize the ubiquitous power-law phenomena. In this paper, identifying
source function of subdiffusion with noisy data using L1 approximation in deep
neural network is presented. In particular, two types of networks for improving
the generalization of the subdiffusion problem are designed with noisy data.
The numerical experiments are given to illustrate the availability using deep
learning. To the best of our knowledge, this is the first topic on the
discovery of subdiffusion in deep learning with noisy data.
