Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

TL;DR

This paper introduces a Bayesian calibration method for coupled computational mechanics models using interface deformation data, accounting for uncertainties and employing Gaussian process regression to reduce computational costs.

Contribution

It presents a novel Bayesian framework for calibrating coupled models with interface deformation data, incorporating uncertainty quantification and efficient likelihood learning.

Findings

Statistically based discrepancy measure yields the most expressive posterior.

The approach effectively handles high-dimensional parameter spaces.

Application to biofilm fluid-structure interaction models demonstrates practical utility.

Abstract

Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement data of material points is available. The interpretation of such a calibration problem as a statistical inference problem, in contrast to deterministic model calibration, is computationally more robust and allows the analyst to find a posterior distribution over possible solutions rather than a single point estimate. The proposed framework also enables the consideration of unavoidable uncertainties that are present in every experiment and are expected to play an important role in the model calibration process. To mitigate the computational costs of expensive forward model evaluations, we propose to learn the log-likelihood function from a controllable amount of parallel simulation runs using Gaussian process regression. We introduce and specifically study the effect of three different discrepancy measures for deformed interfaces between reference data and simulation. We show that a statistically based discrepancy measure results in the most expressive posterior distribution. We further apply the approach to numerical examples in higher model parameter dimensions and interpret the resulting posterior under uncertainty. In the examples, we investigate coupled multi-physics models of fluid-structure interaction effects in biofilms and find that the model parameters affect the results in a coupled manner.