Artificial neural networks for solving elliptic differential equations with boundary layer
DOI10.1002/mma.8192zbMath1529.35277OpenAlexW4220859601MaRDI QIDQ6071007
Dongfang Yuan, Fujun Cao, Yongbin Ge, Guimei Cui, Wen-Hui Liu, Lin Shi
Publication date: 27 November 2023
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.8192
Learning and adaptive systems in artificial intelligence (68T05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Rate of convergence, degree of approximation (41A25) Approximation by other special function classes (41A30) Elliptic equations and elliptic systems (35J99)
Cites Work
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- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
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- DGM: a deep learning algorithm for solving partial differential equations
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- Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
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