Fixed Inducing Points Online Bayesian Calibration for Computer Models with an Application to a Scale-Resolving CFD Simulation

TL;DR

This paper introduces FIPO-BC, an efficient online Bayesian calibration method using fixed inducing points, which significantly reduces computational costs and enables real-time model calibration, demonstrated on turbulence modeling and simple functions.

Contribution

The paper presents a novel fixed inducing points approach for online Bayesian calibration, improving efficiency and enabling real-time updates compared to traditional methods.

Findings

FIPO-BC achieves at least ten times faster calibration than STD-BC.

FIPO-BC provides similar results to STD-BC with sufficiently fine inducing points.

The online feature allows continuous model updating, reducing database generation workload.

Abstract

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.