One of the key strengths of neural networks lies in their ability to perform complex non-linear mappings between input and output data. This work focuses on training a neural network to determine the optimal unit cell topology corresponding to a specific constitutive elastic matrix. The neural network, designed to reverse the homogenization process, establishes a link between the unit cell's shape and its elastic properties. Utilizing a diverse range of geometries, a dataset was developed, that correlates elastic properties with their respective geometries. This dataset was then used to construct and train a feed-forward neural network using the deep learning toolbox available in MATLAB. The study involved homogenizing all geometries under periodic boundary conditions. The lattice was modeled as a biphasic material where the solid phase inherited the material properties, and the rest of the representative volume element (RVE) was treated as a void phase, assigned 1e-06 of the solid material's Young's modulus. For the effective imposition of periodic boundary conditions, a uniform mesh of 2D quadrilateral elements was employed. The neural network demonstrates its prowess by proposing suitable unit cells. Its ability to non-linearly map the relationship between a unit cell's elastic properties and its geometry significantly reduces the computational burden associated with conducting structural optimizations. This process effectively produces unit cells that possess the desired properties.