Discovery of subdiffusion problem with noisy data via deep learning

  title={Discovery of subdiffusion problem with noisy data via deep learning},
  author={Xingjian Xu and Minghua Chen},
  journal={J. Sci. Comput.},
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 timefractional PDEs, which can effectively characterize the ubiquitous… 



Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

  • M. Raissi
  • Computer Science
    J. Mach. Learn. Res.
  • 2018
This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.

Convergence Rate Analysis for Deep Ritz Method

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A Deep Learning Based Discontinuous Galerkin Method for Hyperbolic Equations with Discontinuous Solutions and Random Uncertainties

The D2GM is found numerically to be first-order and second-order accurate for (stochastic) linear conservation law with smooth solutions using piecewise constant and piecewise linear basis functions, respectively.

Solving Fokker-Planck equation using deep learning.

Penalty factors are introduced to overcome the local optimization for the deep learning approach to solve the general FP equations based on deep neural networks, and the corresponding setting rules are given.

DGM: A deep learning algorithm for solving partial differential equations

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