  We develop a fast multi-fidelity modeling method for very complex
correlations between high- and low-fidelity data by working in modal space to
extract the proper correlation function. We apply this method to infer the
amplitude of motion of a flexible marine riser in cross-flow, subject to
vortex-induced vibrations (VIV). VIV are driven by an absolute instability in
the flow, which imposes a frequency (Strouhal) law that requires a matching
with the impedance of the structure; this matching is easily achieved because
of the rapid parametric variation of the added mass force. As a result, the
wavenumber of the riser spatial response is within narrow bands of uncertainty.
Hence, an error in wavenumber prediction can cause significant phase-related
errors in the shape of the amplitude of response along the riser, rendering
correlation between low- and high-fidelity data very complex. Working in modal
space as outlined herein, dense data from low-fidelity data, provided by the
semi-empirical computer code VIVA, can correlate in modal space with few
high-fidelity data, obtained from experiments or fully-resolved CFD
simulations, to correct both phase and amplitude and provide predictions that
agree very well overall with the correct shape of the amplitude response. We
also quantify the uncertainty in the prediction using Bayesian modeling and
exploit this uncertainty to formulate an active learning strategy for the best
possible location of the sensors providing the high fidelity measurements.
