NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Leung, Wing Tat; Lin, Guang; Zhang, Zecheng

doi:10.1016/j.jcp.2022.111539

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Journal Article · Sat Aug 27 00:00:00 EDT 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111539· OSTI ID:2421760

Leung, Wing Tat ^[1]; ^[2]; Zhang, Zecheng ^[2]

City Univ. of Hong Kong, Kowloon (Hong Kong); OSTI
Purdue Univ., West Lafayette, IN (United States)

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization approximates a multiscale equation by a homogenized equation without multiscale property; it includes solving cell problems and the homogenized equation. The cell problems are periodic, and we propose an oversampling strategy that significantly improves the PINN accuracy on periodic problems. The homogenized equation has a constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method, neural homogenization based PINN (NH-PINN), to improve the PINN accuracy for solving multiscale problems with the help of homogenization.

View Accepted Manuscript (DOE)

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0021142

OSTI ID:: 2421760

Alternate ID(s):: OSTI ID: 1885864

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 470; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (16)

A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media Hou, Thomas Y.; Wu, Xiao-Hui Journal of Computational Physics, Vol. 134, Issue 1 https://doi.org/10.1006/jcph.1997.5682	journal	June 1997
A multi-stage deep learning based algorithm for multiscale model reduction Chung, Eric; Leung, Wing Tat; Pun, Sai-Mang Journal of Computational and Applied Mathematics, Vol. 394 https://doi.org/10.1016/j.cam.2021.113506	journal	October 2021
Constraint Energy Minimizing Generalized Multiscale Finite Element Method Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat Computer Methods in Applied Mechanics and Engineering, Vol. 339 https://doi.org/10.1016/j.cma.2018.04.010	journal	September 2018
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Wang, Sifan; Wang, Hanwen; Perdikaris, Paris Computer Methods in Applied Mechanics and Engineering, Vol. 384 https://doi.org/10.1016/j.cma.2021.113938	journal	October 2021
Generalized multiscale finite element methods (GMsFEM) Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. Journal of Computational Physics, Vol. 251 https://doi.org/10.1016/j.jcp.2013.04.045	journal	October 2013
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. Journal of Computational Physics, Vol. 320 https://doi.org/10.1016/j.jcp.2016.04.054	journal	September 2016
Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat Journal of Computational Physics, Vol. 371 https://doi.org/10.1016/j.jcp.2018.05.041	journal	October 2018
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data Yang, Liu; Meng, Xuhui; Karniadakis, George Em Journal of Computational Physics, Vol. 425 https://doi.org/10.1016/j.jcp.2020.109913	journal	January 2021
Computational multiscale methods for quasi-gas dynamic equations Chetverushkin, Boris; Chung, Eric; Efendiev, Yalchin Journal of Computational Physics, Vol. 440 https://doi.org/10.1016/j.jcp.2021.110352	journal	September 2021
Asymptotic and numerical homogenization Engquist, B.; Souganidis, P. E. Acta Numerica, Vol. 17 https://doi.org/10.1017/S0962492906360011	journal	April 2008
Modeling of subgrid effects in coarse-scale simulations of transport in heterogeneous porous media Efendiev, Y.; Durlofsky, L. J.; Lee, S. H. Water Resources Research, Vol. 36, Issue 8 https://doi.org/10.1029/2000WR900141	journal	August 2000
Convergence of a Nonconforming Multiscale Finite Element Method Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui SIAM Journal on Numerical Analysis, Vol. 37, Issue 3 https://doi.org/10.1137/S0036142997330329	journal	January 2000
An Efficient Two-Stage Sampling Method for Uncertainty Quantification in History Matching Geological Models Ma, Xianlin; Al-Harbi, Mishal; Datta-Gupta, Akhil SPE Journal, Vol. 13, Issue 01 https://doi.org/10.2118/102476-PA	journal	March 2008
Multiphysics and Multiscale Methods for Modeling Fluid Flow Through Naturally Fractured Carbonate Karst Reservoirs Popov, P.; Qin, G.; Bi, L. SPE Reservoir Evaluation & Engineering, Vol. 12, Issue 02 https://doi.org/10.2118/105378-PA	journal	April 2009
Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations Zhang, Zecheng; Chung, Eric T.; Efendiev, Yalchin Mathematics, Vol. 8, Issue 5 https://doi.org/10.3390/math8050720	journal	May 2020

Similar Records

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Journal Article · Wed Jun 19 20:00:00 EDT 2024 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:2425908

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Journal Article · Fri Feb 28 19:00:00 EST 2025 · Communications in Computational Physics · OSTI ID:2571702

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Journal Article · Thu Mar 17 20:00:00 EDT 2022 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1976976

Related Subjects

97 MATHEMATICS AND COMPUTING
Computer Science
Homogenization
Multiscale partial differential equation
Physics
Physics-informed neural network

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Citation Formats

References (16)

Similar Records

Related Subjects