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Physics-informed neural network (PINN) is a data-driven approach to solveequations.  It is successful in many applications; however, the accuracy of the PINN isnot satisfactory when it is used to solve multiscale equations.  Homogenization is a way of approximating a multiscale equation by ahomogenized equation without multiscale property; it includes solving cellproblems and the homogenized equation.  The cell problems are periodic; and we propose an oversampling strategy whichgreatly improves the PINN accuracy on periodic problems.  The homogenized equation has constant or slow dependency coefficient and canalso be solved by PINN accurately.  We hence proposed a 3-step method to improve the PINN accuracy for solvingmultiscale problems with the help of the homogenization.  We apply our method to solve three equations which represent three differenthomogenization.  The results show that the proposed method greatly improves the PINN accuracy.  Besides, we also find that the PINN aided homogenization may achieve betteraccuracy than the numerical methods driven homogenization; PINN hence is apotential alternative to implementing the homogenization.

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