  We develop a novel multi-fidelity framework that goes far beyond the
classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000). Our method can
handle general discontinuous cross-correlations among systems with different
levels of fidelity. A combination of multi-fidelity Gaussian Processes (AR(1)
Co-kriging) and deep neural networks enables us to construct a method that is
immune to discontinuities. We demonstrate the effectiveness of the new
technology using standard benchmark problems designed to resemble the outputs
of complicated high- and low-fidelity codes.
