Fixed Inducing Points Online Bayesian Calibration for Computer Models with an Application to a Scale-Resolving CFD Simulation
This incremental improvement addresses computational bottlenecks for researchers and engineers using Bayesian calibration in fields like computational fluid dynamics.
The paper tackles the computational inefficiency and lack of online learning in standard Bayesian calibration for expensive models by proposing the FIPO-BC algorithm, which uses fixed inducing points to achieve similar results while being at least ten times faster and enabling continuous updates.
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.