  With the advancements of computer architectures, the use of computational
models proliferates to solve complex problems in many scientific applications
such as nuclear physics and climate research. However, the potential of such
models is often hindered because they tend to be computationally expensive and
consequently ill-fitting for uncertainty quantification. Furthermore, they are
usually not calibrated with real-time observations. We develop a
computationally efficient algorithm based on variational Bayes inference (VBI)
for calibration of computer models with Gaussian processes. Unfortunately, the
speed and scalability of VBI diminishes when applied to the calibration
framework with dependent data. To preserve the efficiency of VBI, we adopt a
pairwise decomposition of the data likelihood using vine copulas that separate
the information on dependence structure in data from their marginal
distributions. We provide both theoretical and empirical evidence for the
computational scalability of our methodology and describe all the necessary
details for an efficient implementation of the proposed algorithm. We also
demonstrate the opportunities given by our method for practitioners on a real
data example through calibration of the Liquid Drop Model of nuclear binding
energies.
