Adaptive partition of unity networks (APUNet): a localized deep learning method for solving PDEs

Author:

Barbara Idriss,Masrour TawfikORCID,Hadda Mohammed

Publisher

Springer Science and Business Media LLC

Subject

Control and Optimization,Computer Science Applications,Modeling and Simulation,Control and Systems Engineering

Reference31 articles.

1. Al-Aradi A, Correia A, Naiff D, Jardim G, Saporito Y (2018) Solving nonlinear and high-dimensional partial differential equations via deep learning. arXiv preprint arXiv:1811.08782

2. Al-Aradi A, Correia A, Jardim G, Freitas Naiff D, Saporito Y (2022) Extensions of the deep Galerkin method. Appl Math Comput 430:127287

3. Babuška I, Melenk JM (1997) The partition of unity method. Int J Numer Methods Eng 40(4):727–758

4. Beck C, Hutzenthaler M, Jentzen A, Kuckuck B (2020) An overview on deep learning-based approximation methods for partial differential equations. arXiv preprint arXiv:2012.12348

5. Blechschmidt J, Ernst OG (2021) Three ways to solve partial differential equations with neural networks?a review. GAMM-Mitteilungen 44(2):202100006

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