Physics-informed neural network (PINN) is a data-driven approach to solve 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 is a way of approximating 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 which greatly improves the PINN accuracy on periodic problems. The homogenized equation has constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method to improve the PINN accuracy for solving multiscale problems with the help of the homogenization. We apply our method to solve three equations which represent three different homogenization. The results show that the proposed method greatly improves the PINN accuracy. Besides, we also find that the PINN aided homogenization may achieve better accuracy than the numerical methods driven homogenization; PINN hence is a potential alternative to implementing the homogenization.

翻译：物理知情神经网络(PINN)是解决方程式的数据驱动方法。 它在许多应用中是成功的; 但是, 当用于解决多尺度方程式时, PINN 的准确性并不令人满意。 智化是一种通过没有多尺度属性的同质方程式来接近多尺度方程式的方法; 它包括解决单元格问题和同质方程式。 细胞问题是周期性的; 我们提出一个过度抽样战略, 大大改进PINN周期问题的准确性。 普通化方程式具有恒定或缓慢的依赖系数, 并且也可以由 PINN 准确地解决。 因此, 我们提出了一个三步方法来提高 PINN 的精确性, 以便在同质化的帮助下解决多尺度问题。 我们用这个方法来解决三个代表三种不同的同质化的方程式。 结果表明, 拟议的方法大大提高了PINN的准确性。 此外, 我们还发现, PINN 辅助的同质化可能比以同质化的数字方法更准确性化; 因此, PINN 是实施同质化的一种可能的替代办法。