Bayesian Updating of constitutive parameters under hybrid uncertainties with a novel surrogate model applied to biofilms

Authored by

Lukas Fritsch, Hendrik Geisler, Jan Grashorn, Felix Klempt, Meisam Soleimani, Matteo Broggi, Philipp Junker, Michael Beer

Abstract

Accurate modeling of bacterial biofilm growth is essential for understanding their complex dynamics in biomedical, environmental, and industrial settings. These dynamics are shaped by a variety of environmental influences, including the presence of antibiotics, nutrient availability, and inter-species interactions, all of which affect species-specific growth rates. However, capturing this behavior in computational models is challenging due to the presence of hybrid uncertainties, a combination of epistemic uncertainty (stemming from incomplete knowledge about model parameters) and aleatory uncertainty (reflecting inherent biological variability and stochastic environmental conditions). In this work, we present a Bayesian model updating (BMU) framework to calibrate a recently introduced multi-species biofilm growth model. To enable efficient inference in the presence of hybrid uncertainties, we construct a reduced-order model (ROM) derived using the Time-Separated Stochastic Mechanics (TSM) approach. TSM allows for an efficient propagation of aleatory uncertainty, which enables single-loop Bayesian inference, thereby avoiding the computationally expensive nested (double-loop) schemes typically required in hybrid uncertainty quantification. The BMU framework employs a likelihood function constructed from the mean and variance of stochastic model outputs, enabling robust parameter calibration even under sparse and noisy data. We validate our approach through two case studies: a two-species and a four-species biofilm model. Both demonstrate that our method not only accurately recovers the underlying model parameters but also provides predictive responses consistent with the synthetic data.

Details

Organisation(s): Institute for Risk and Reliability
International RTG 2657: Computational Mechanics Techniques in High Dimensions
Institute of Continuum Mechanics
External Organisation(s): Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg (HSU)
University of Liverpool
Tongji University
Type: Article
Journal: Computational mechanics
Volume: 78
Pages: 761-782
No. of pages: 22
ISSN: 0178-7675
Publication date: 08.2026
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-026-02777-8 (Access: Open )