Thermo-plastic membrane mirrors could be used to realize very large reflective apertures needed for imaging distant objects at high spatial resolution. The dynamics of deployment of membrane mirrors in space is complex and hard to predict with physics based numerical simulations. Several factors such as local thermal gradient, solar radiation pressure, undamped vibration modes and membrane wrinkling effects need to be accounted for. An integrated architecture is required for multi-disciplinary design and optimization of such membrane structures. This paper investigates data driven methods and their ability to accurately learn and predict patterns that may lead to greater efficiency than conventional physical models. Of particular interest are understanding geometric and boundary factors that may lead to a desired inflated membrane shape. Our present work attempts build and train a deep neural network model with accurate predictions of inflated membrane shape with initial and boundary conditions. Numerical simulations are used to train and optimize the network. Membrane shape measurement data in the form of W-curves is used to train a deep neural network that has been used as a universal function approximator. For the present work, we focus on structural design factors determining the final shape of the inflated membranes. As an on-going effort, an experimental apparatus has been developed to make membrane shape measurements using photogrammetry. Experimental data shall be used to further refine the predictive model ad to verify its outputs. Predictions for expected inflated shapes for varying boundary conditions will be used to develop optimal boundary configurations and alternate feasible membrane geometries. This work aims to provide an alternate data driven approach leading to a multi-objective design and optimization of membrane structures for high frequency optical applications.