Physics-Informed Neural Networks (PINNs) offer a powerful approach for solving differential equations by integrating physical laws directly into the training process, specifically into the loss function. This study explores the application of both PINNs and traditional artificial neural networks (ANNs) to simulate pressure behavior, modeled by the diffusion equation, which is key to reservoir characterization through well pressure tests. Two scenarios are analyzed: in the first, a PINN solves the one-dimensional diffusion equation in Cartesian coordinates, representing linear flow. Its predictions are compared with results obtained using the finite difference method and with the analytical solution. In the second scenario, an ANN is trained with semi-analytical data generated from the Laplace-domain solution of the radial diffusion equation, which is numerically inverted using the Stehfest method. This network accurately reproduces the pressure response during a drawdown test. The results show that both PINNs and ANNs are capable of approximating complex solutions with high fidelity, supporting their potential for pressure test analysis and real-time decision-making in petroleum engineering.