A Bayesian framework for functional calibration of expensive computational models through non-isometric matching

TL;DR

This paper introduces a Bayesian non-isometric matching calibration method that effectively calibrates expensive computational models with limited data, improving prediction accuracy by addressing non-identifiability through geometric and optimization techniques.

Contribution

The paper presents BNMC, a novel Bayesian calibration framework that handles functional calibration with limited samples and resolves identifiability issues via geometric curve-to-surface matching.

Findings

BNMC outperforms existing calibration methods in prediction accuracy.

The approach effectively calibrates expensive models with few evaluations.

Geometric perspective aids in resolving parameter identifiability.

Abstract

We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian non-isometric matching calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process (GP) whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks.