Embedded Model Error Representation for Bayesian Model Calibration

TL;DR

This paper introduces a Bayesian framework using Polynomial Chaos to represent and quantify structural model errors, improving uncertainty quantification in complex physical system models.

Contribution

It develops a non-intrusive, embedded correction method for model error estimation within Bayesian inference, applicable to complex models.

Findings

Effective model error quantification demonstrated on synthetic examples.

Successful application to a chemical ignition problem.

Enhanced separation of model and data uncertainties.

Abstract

Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often the largest contributor to the overall predictive uncertainty. This work builds on a recently developed framework of embedded, internal model correction, in order to represent and quantify structural errors, together with model parameters, within a Bayesian inference context. We focus specifically on a Polynomial Chaos representation with additive modification of existing model parameters, enabling a non-intrusive procedure for efficient approximate likelihood construction, model error estimation, and disambiguation of model and data errors' contributions to predictive uncertainty. The framework is demonstrated on several synthetic examples, as well as on a chemical ignition problem.