Discovery of Subdiffusion Problem with Noisy Data via Deep Learning

Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the problem. Recently, traditional ODEs dynamics using linear multistep methods deep have discussed [Racheal and Du, SIAM J. Numer. Anal. 59 (2021) 429-455; Du et al. arXiv:2103.1148 ]. We extend this framework to data-driven time-fractional PDEs, which can effectively characterize ubiquitous power-law phenomena. In paper, identifying source function subdiffusion with noisy $$L_{1}$$ approximation neural network is presented. particular, two types networks for improving generalization problem are designed data. The numerical experiments given illustrate availability high noise levels learning. To best our knowledge, first topic on