TY - JOUR
T1 - NH-PINN
T2 - Neural homogenization-based physics-informed neural network for multiscale problems
AU - Leung, Wing Tat
AU - Lin, Guang
AU - Zhang, Zecheng
PY - 2022/12/1
Y1 - 2022/12/1
N2 - 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.
AB - 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.
KW - Homogenization
KW - Multiscale partial differential equation
KW - Physics-informed neural network
UR - http://www.scopus.com/inward/record.url?scp=85137013954&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85137013954&origin=recordpage
U2 - 10.1016/j.jcp.2022.111539
DO - 10.1016/j.jcp.2022.111539
M3 - 21_Publication in refereed journal
VL - 470
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 111539
ER -