  Multi-fidelity modeling and calibration are 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. This conversion endows our approach with attractive
advantages such as increased accuracy, reduced costs, flexibility to jointly
fuse any number of data sources, and ability to visualize correlations between
data sources. This visualization allows the user to detect model form errors or
determine the optimum strategy for high-fidelity emulation by fitting LMGP only
to the subset of the data sources that are well-correlated. We also develop a
new kernel function that enables LMGPs to not only build a probabilistic
multi-fidelity surrogate but also estimate calibration parameters with high
accuracy and consistency. The implementation and use of our approach are
considerably simpler and less prone to numerical issues compared to existing
technologies. We demonstrate the benefits of LMGP-based data fusion by
comparing its performance against competing methods on a wide range of
examples.
