论文标题
通过深度学习发现嘈杂数据的次扩散问题
Discovery of subdiffusion problem with noisy data via deep learning
论文作者
论文摘要
通过嵌入发现问题，已经开发出了来自机器学习中观察到的数据的部分微分方程（PDE）的数据驱动的发现。最近，在[Racheal和Du，Siam J. Numer中讨论了使用线性多步法的传统ODES动力学发现。肛门。 59（2021）429-455; Du等。 ARXIV：2103.11488]。我们将此框架扩展到了时间折叠PDE的数据驱动的发现，该发现可以有效地表征无处不在的幂律现象。在本文中，介绍了使用深神经网络中L1近似噪声数据来识别次扩散的源功能。特别是，使用嘈杂的数据设计了两种用于改善次扩散问题概括的网络。进行数值实验以说明使用深度学习的可用性。据我们所知，这是通过嘈杂的数据发现深度学习的第一个主题。
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.
