With the advancement of high-performance computing and sensor technology, it has become possible to directly identify physical laws from data. Although data-driven methods for identifying partial differential equations have demonstrated potential in various fields, their applicability and effectiveness in seepage problems still require systematic evaluation. For this, the PDE(partial differential equations)-LEARN framework based on sparse regression was employed to systematically identify the governing equations for one-dimensional linear, two-dimensional linear, and one-dimensional nonlinear seepage flows. The impacts of data volume and noise level on identification accuracy were investigated. The results indicate that the framework can accurately identify the equation structure even with limited data and under noisy conditions, while maintaining low errors in equation coefficients. Moreover, moderate noise is found to enhance equation identification performance through the stochastic resonance effect. Furthermore, by constructing test cases containing high-order derivative terms, the predictive performance of the identified equations is compared with that of fully connected neural networks, revealing that the former exhibits significant advantages in extrapolation predictions. Finally, the method's applicability to real physical processes is validated through variable-diameter sand-filled tube seepage experiments. The results show that the model predictions are highly consistent with experimental data, demonstrating the potential of this approach in practical seepage modeling.