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

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.