Data Fusion as a Latent Space Learning Problem

Multi-fidelity modeling and calibration are two data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned purely based on the data. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, and flexibility to jointly fuse any number of data sources. Additionally, the learned latent space in our approach compactly visualizes the correlations between data sources which allows designers and engineers to detect model form errors or determine the optimum strategy for high-fidelity emulation by only fusing correlated or sufficiently accurate data sources. We also develop a new correlation function that enables LMGPs to estimate calibration parameters with high accuracy and consistency even in the presence of unbalanced and noisy datasets. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing data fusion technologies. We demonstrate the benefits of LMGP-based data fusion on a wide range of analytic examples. by comparing its performance against existing technologies.