Bio-composite materials are environmentally friendly and sustainable due to their degradability, and some bio-composites also exhibit corrosion resistance. However, the water absorption properties of materials largely determine their corrosion resistance and practical applications. Improving water resistance through material design is therefore necessary. Experimental optimization is slow and costly. Numerical simulations offer a faster alternative. Mixed finite element methods improve flux accuracy by solving field variables independently, but they introduce additional degrees of freedom and become computationally expensive for repeated simulations. To overcome these limitations, a Physics-Informed Convolutional Neural Network (PICNN) is developed within a multi-field variational framework. The model adopts an encoder–decoder architecture with densely connected convolutional blocks to efficiently capture complex physical features. To improve flux accuracy, a gradient-enhanced term, derived from a multi-field variational formulation, is incorporated into the loss function. This term is enforced together with constitutive relations, continuity equations, and boundary conditions, acting as a variational regularization that stabilizes the solution. It is worth mentioning that the PICNN is label-free and does not require high-quality labeled datasets. The gradient term derived from the multi-field variational formulation plays a crucial role in improving flux accuracy. In the PICNN, it acts as a variational regularization term in the loss function, weighted by a Lagrange multiplier, and effectively suppresses interfacial oscillations. The proposed PICNN achieves substantially higher computational efficiency than Finite Element Method (FEM) while maintaining similar results compared with FEM solutions. The efficiency increases with the number of repeated simulations, as the inference cost scales approximately linearly. Variations in particle shapes and packing configurations are included during training, enabling strong generalization across diverse micro-structural realizations.