The objective of this work is to predict grid-level flow fields in porous media as a priori to determining the permeability of porous media.A physics-informed ML model is developed by using the results from numerical fluid flow simulations of randomly distributed circular grains to represent the porous media. The deep U-Net and ResNet neural network architectures are combined to train a deep learning model that avoids vanishing gradient issues. The model integrates continuity and momentum conservation equations into the loss function to ensure physical consistency. Additionally, we modify the padding function in convolutional layers to use circular paddings, mimicking periodic boundary conditions in LB simulations. By learning inter-grid communications, the ML model achieves precise flow predictions for new simulation sets with high accuracy. The robustness of the developed model is then tested for numerous variations of porous media that have not been used for developing the model.