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

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Original languageEnglish
Article number111539
Journal / PublicationJournal of Computational Physics
Online published27 Aug 2022
Publication statusPublished - 1 Dec 2022


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.

Research Area(s)

  • Homogenization, Multiscale partial differential equation, Physics-informed neural network