An industrial design process is often highly iterative. With unclear relationships among QoI trade-offs and the design solution, the definition of the cost function usually undergoes several Modifications that mandates a continued interaction between the designer and the client to encode all design and mission requirements into an optimization-friendly mathematical formulation. Such an iterative process is time-consuming and computationally expensive. An efficient way to accelerate the process is to derive data-driven mappings between the design/mission and QoI spaces to provide visual insights into the interactions among different QoIs as related to their corresponding simulation parameters. In this paper, we propose Shared-GP, a generative model for the design process that is based on a Gaussian process latent variable model formulation. Shared-GP learns correlations within and across multiple, but implicitly correlated, data spaces considered in the design process (i.e., the simulation parameter space, the design space, and the QoI spaces) to provide data-driven mappings across these data spaces via efficient inference. Shared-GP also provides a structured low-dimensional representation shared among the data spaces (some of which are of very high dimension) that the designer can use to efficiently explore the design space without the need for costly simulations. Experiments demonstrate that our model is capable of not only parameterizing multiple QoIs but also providing accurate estimates given the simulation parameters or some given/observed QoIs compared with deep learning models and other Gaussian process variants.