<p>Accurate prediction of pressure diffusion in heterogeneous porous media is essential for production forecasting, reservoir behavior analysis, and field development. Physics-based numerical simulators provide reliable pressure solutions, but their computational cost can become limiting for high-resolution heterogeneous models or repeated forward simulations. In this work, a graph neural-network (GNN)-based surrogate model is developed to predict final-time pressure distributions in heterogeneous porous media. Training data are generated by solving the pressure-diffusion equation on an unstructured triangular mesh with spatially varying permeability derived from lithology samples. The mesh is represented as a graph, where nodes contain spatial coordinates, pressure-related inputs, boundary-condition information, and permeability values, while edges represent local mesh connectivity. An edge-based pressure-gradient loss is evaluated as a physics-guided regularization term to encourage local pressure-gradient consistency across connected mesh nodes. The model is evaluated using held-out test cases, independent training runs and additional cross-lithology tests in which models trained on one lithology slice are evaluated on five unseen slices. These evaluations assess predictive accuracy, stability, spatial error behavior, and computational efficiency. The results show that the surrogate reproduces the dominant pressure front and pressure magnitude with low error relative to the full pressure range, while reducing prediction time by approximately 47 times compared with the finite-element solver. The cross-lithology tests achieved a mean unseen-lithology <i>R</i>² of 0.9199, indicating that the model retains predictive capability on previously unseen permeability realizations. The remaining errors are spatially localized, indicating where future graph-structure improvements such as permeability-informed edge weights should be examined.</p>