Mechanical metamaterials are materials that appear to have unusual elastic mechanical properties, with the most prominent being a negative Poisson’s ratio. The key to their unique properties lies in the microarchitecture of the material rather than the material itself. For advanced applications in the realm of prosthetics, such as form matching, aperiodic metamaterials have been recommended above repetitive ones. In a restricted lattice, metamaterials with disordered microarchitecture have displayed a wide variety of anisotropic conventional and auxetic behaviour. Because of the non-unique and non-intuitive link between the random network (RN) structures and their mechanical responses, their inverse design, which tries to extract the ideal structure according to specified requirements, remains a complex process. The current study looks at the forward prediction of mechanical response and the inverse design of 2D random network metamaterial unit cells for use in aperiodic combinatorial designs. The associated mechanical properties of stiffness and Poisson's ratio in two directions were numerically simulated for the unit cells. The configuration of random network designs that provide the least complicated unit cells with the greatest range of mechanical properties were selected. A dataset of such unit cells and their mechanical responses was then created for training machine learning models. A forward predictor of their mechanical response through a regression model was trained, to accelerate the production of the datasets and assist in the inverse design modelling. It was suggested to model the inverse design issue in a probabilistically generative manner, allowing for an interpretable investigation of the complicated structure–performance connection. A variational autoencoder (VAE) was trained to map complex microstructures into a low-dimensional, continuous, and organized latent space based on their mechanical response. A systematic approach to train machine learning models was investigated based on hyperparameter optimization methods, with cross-validation and a search space that expands over the model hyperparameters and data analysis alternatives. The trained forward predictor and generative model were evaluated, and the reported R^2 values were 0.99 and 0.96, respectively. Compared to numerical simulations, the estimation of mechanical properties through the regressor resulted in a hundredfold acceleration of the process. The trained deep generative model can be an effective tool for expediting the creation of RN unit cells. On-demand inverse creation of metamaterials for both observable and intentionally designed mechanical responses is achievable. To illustrate a practical use of such unit cells, a technique for aperiodic combinatorial design of unit cells for 2D form matching on two directions and all four sides was also provided. The mechanical properties of the unit cells, as well as the combinatorial design capabilities, were evaluated using experimental tests of 3D printed specimens. The experimental results of the unit cells were in good agreement with the numerical simulations. Similar forms to those programmed were achieved by tensioning the combinatorial patterns, albeit with a less degree of distortion. Overall, the findings show the RN unit cells' potential for combinatorial design.