A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction

DOI10.1137/19M1277485zbMath1459.35194arXiv1907.00806OpenAlexW3045668026WikidataQ114074240 ScholiaQ114074240MaRDI QIDQ5150066

Sijing Li, Zhiwen Zhang, Hong-Kai Zhao

Publication date: 9 February 2021

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.00806

zbMATH Keywords

Green's functionneural networkproper orthogonal decompositionuncertainty quantificationmultiscale elliptic PDEs with random coefficients

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with randomness, stochastic partial differential equations (35R60) Quasilinear elliptic equations (35J62) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80) Model reduction in optics and electromagnetic theory (78M34)

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