Abstarct: Reconstructing high-resolution flow fields in experimental fluid mechanics is a complex challenge due to sparse and incomplete data in time and space. This issue is exacerbated by the limitations of current experimental tools and methods, which leave key areas without measurable data. In this research, a practical solution to this problem is proposed by utilizing physics-informed neural networks (PINNs) with an inverse approach to integrate sparse data with physical laws. To evaluate the capability of these networks in solving fluid flow problems in simple porous media, differential equations related to fluid flow were first solved using numerical methods such as finite element and finite difference. This step generated reference data to create datasets needed for training the PINNs. Additionally, these datasets were used to compare the final results of this model with numerical solutions. Next, a physics-informed neural network was implemented. This model was a multilxayer perceptron with reference data as input. Furthermore, physical laws and boundary and initial conditions were added as training constraints to ensure that the learning process of the network accurately aligned with the physical behavior of the fluid flow. During this phase, various activation functions were tested, and ultimately, the hyperbolic tangent function was selected for modeling. Different optimizers, including Adam and L-BFGS, were also utilized to ensure that the results closely matched those generated by numerical methods. For the single-phase case, a one-dimensional fluid flow model in a pipe was initially simulated using the Navier-Stokes equation. The evaluation metrics included the root mean square error (0.0275), the coefficient of determination (0.997), and the correlation coefficient (0.996). Then, using COMSOL software, a two-dimensional model was developed for fluid flow in a more complex environment. Three datasets with varying densities were generated from this simulation, and the results of the first two datasets closely matched the results from the COMSOL model. In further examinations, for a dataset with 28 sensors around a cylinder, the coefficient of determination and the root mean square error for the horizontal and vertical velocity components were 0.996 and 0.0251, and 0.969 and 0.0169, respectively. For the two-phase case, the advection-diffusion equation was investigated in one-dimensional and two-dimensional states, and the required data was computed through finite difference simulations. Then, a subset of this data was used to train the model, resulting in a cost function of 6.1×〖10〗^(-5) for the one-dimensional case and 8.7×〖10〗^(-4) for the two-dimensional case. The relative L2-norm error was calculated to be 0.175% for the one-dimensional case and 0.28% for the two-dimensional case. The final results showed that the physics-informed neural network effectively reconstructed fluid flow profiles even under data-scarce conditions, and successfully addressed differential equation problems and flow behavior prediction in porous media with results in agreement with numerical solutions. This surrogate model not only enables the recovery of velocity fields throughout the desired domain with high accuracy but also provides results that are consistent with numerical solutions, demonstrating its potential for analyzing complex flows in porous media.