Shared-Gaussian Process: Learning Interpretable Shared Hidden Structure Across Data Spaces for Design Space Analysis and Exploration

An industrial design process is often highly iterative. With unclear relationships between the quantity of interest (QoI) trade-offs and the design solution, the definition of the cost function usually undergoes several modifications that mandate 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 this 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-Gaussian process (GP), a generative model for the design process that is based on a Gaussian process latent variable model. 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 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.