  This study used a multigrid-based convolutional neural network architecture
known as MgNet in operator learning to solve numerical partial differential
equations (PDEs). Given the property of smoothing iterations in multigrid
methods where low-frequency errors decay slowly, we introduced a low-frequency
correction structure for residuals to enhance the standard V-cycle MgNet. The
enhanced MgNet model can capture the low-frequency features of solutions
considerably better than the standard V-cycle MgNet. The numerical results
obtained using some standard operator learning tasks are better than those
obtained using many state-of-the-art methods, demonstrating the efficiency of
our model.Moreover, numerically, our new model is more robust in case of low-
and high-resolution data during training and testing, respectively.
