  This paper proposes a novel fixed inducing points online Bayesian calibration
(FIPO-BC) algorithm to efficiently learn the model parameters using a benchmark
database. The standard Bayesian calibration (STD-BC) algorithm provides a
statistical method to calibrate the parameters of computationally expensive
models. However, the STD-BC algorithm scales very badly with the number of data
points and lacks online learning capability. The proposed FIPO-BC algorithm
greatly improves the computational efficiency and enables the online
calibration by executing the calibration on a set of predefined inducing
points.
  To demonstrate the procedure of the FIPO-BC algorithm, two tests are
performed, finding the optimal value and exploring the posterior distribution
of 1) the parameter in a simple function, and 2) the high-wave number damping
factor in a scale-resolving turbulence model (SAS-SST). The results (such as
the calibrated model parameter and its posterior distribution) of FIPO-BC with
different inducing points are compared to those of STD-BC. It is found that
FIPO-BC and STD-BC can provide very similar results, once the predefined set of
inducing point in FIPO-BC is sufficiently fine. But, the FIPO-BC algorithm is
at least ten times faster than the STD-BC algorithm. Meanwhile, the online
feature of the FIPO-BC allows continuous updating of the calibration outputs
and potentially reduces the workload on generating the database.
