The recently introduced neural network structure, known as the Kolmogorov-Arnold Network (KAN), provides greater interpretability and accuracy compared to ordinary Multi-Layer Perceptrons (MLPs) due to its use of spline functions. The primary goal of this research is to propose a novel Physics-Informed Neural Network (PINN) architecture based on KAN for solving the Buckley-Leverett equation, aiming to study its performance versus a conventional MLP-based PINN. We conducted a comparative analysis between the KAN and MLP architectures. We found that they both achieved comparable accuracy. However, the KAN’s training process is approximately twice as time-consuming as that of the MLP. When validating with experimental data, the KAN architecture showed enhanced robustness when trained with a hybrid optimizer approach that combines the Adam and L-BFGS optimizers rather than using L-BFGS alone. Moreover, increasing the number of layers and neurons in the KAN model improved its predictions, nearly matching the MLP-based PINN results for modeling the laboratory experiment. The results highlight the promising potential of KAN-based PINNs, especially when optimized architectures and hybrid training approaches are used for modeling fluid dynamics in porous media.