Coupled hydromechanical finite-element modeling of granular soils, taking into account internal erosion, is computationally prohibitive. Alternative data-driven approaches require large data sets for training and often provide poor generalization ability. To overcome these issues, this study proposed a physics-informed multifidelity residual neural network (PI-MR-NN) modeling strategy. The model was first trained using low-fidelity data to focus on capturing the main underpinning physical laws. Subsequent training on sparser high-fidelity data was then used to calibrate and refine the model. Physical constraints, e.g., boundary conditions, were incorporated through modifications to the loss functions. Feedforward and long short-term memory neural networks were considered as the baseline algorithms for training models. The PI-MR-NN was first used to reproduce synthetic results generated by the soil constitutive model SIMSAND and a published internal erosion model. The developed data-driven model was then applied to simulate the breach of a practical dike-on-foundation case and to predict its temporal responses. All results indicated that the hydromechanical response of porous media can be accurately captured using the proposed PI-MR-NN model. The novel training strategy mitigates the dependency of model performance on the training data set and architecture of the neural network, and the use of physical constraints improves training efficiency and enhances the model’s predictive robustness.