FDM-PINN: Physics-informed neural network based on fictitious domain method. Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Yang, Qihong; Yang, Yu; Cui, Tao; He, Qiaolin
• Is Part Of: International journal of computer mathematics. Volume 100:Issue 3(2023)
• Page Start: 511
• Page End: 524
• Publication Date: 2023-03-04
• Subjects: Fictitious domain method -- neural network -- Robin boundary condition -- automatic differentiation -- elliptic problem; 76-10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2128674
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this article, we present a physics-informed neural network combined with fictitious domain method (FDM-PINN) to study linear elliptic and parabolic problems with Robin boundary condition. Our goal here to develop a deep learning framework where one solves a variant of the original problem on the full Ω, followed by a well-chosen correction on small domain ω ( ω ¯ ⊂ Ω ), which is geometrically simple shaped domain. We study the applicability and accuracy of FDM-PINN for the elliptic and parabolic problems with fixed ω or moving ω . This method is of the virtual control type and relies on a well-designed neural network. Numerical results obtained by FDM-PINN for two-dimensional elliptic and parabolic problems are given, which are more accurate than the results obtained by least-squares/fictitious domain method in [R. Glowinski and Q. He, A least-squares/fictitious domain method for linear elliptic problems with robin boundary conditions, Commun. Comput. Phys. 9 (2011), pp. 587–606.].