Bayesian Updating of Constitutive Parameters under Hybrid Uncertainty using a Reduced-Order Model for Bacterial Biofilms
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Continuum models of multi-species biofilms describe growth, interactions and antibiotic response, but their predictive use is limited by poorly known constitutive parameters and pronounced biological variability. This study considers a recent multi-species biofilm model derived from the extended Hamilton principle, whose material parameters govern nutrient-driven growth and antibiotic-induced degradation. These parameters are affected by both epistemic uncertainty from limited data and aleatory uncertainty from inherent variability, which is represented as hybrid uncertainties using parametric probability-boxes. Classical Bayesian model updating becomes computationally expensive for such models because hybrid uncertainty typically requires nested Monte Carlo simulations. A Bayesian updating framework is developed that combines a p-box description of constitutive parameters with a reduced-order surrogate based on Time-Separated Stochastic Mechanics. This surrogate provides a time-dependent Taylor approximation around the mean parameters and allows efficient computation of mean and variance of the stochastic response in a single forward run. This enables single-loop Bayesian inference using a Gaussian likelihood on summary statistics of biofilm volume fractions at selected times. Two numerical case studies are considered. For a two-species biofilm with five unknown parameters, the approach recovers the true parameter means, identifies strong parameter correlations and captures nonlinear amplification of aleatory variability. For a four-species biofilm with 14 parameters, a hierarchical updating strategy, where two-species submodels are calibrated first and remaining interaction terms are then inferred, yields sharp posteriors, good agreement with synthetic data and robust predictions under time-dependent antibiotic exposure.
