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.

翻译：准确建模细菌生物膜生长对于理解其在生物医学、环境和工业场景中的复杂动力学至关重要。这些动力学受多种环境因素影响，包括抗生素的存在、营养物可用性以及种间相互作用，所有这些因素均会影响物种特异性生长速率。然而，在计算模型中捕捉此类行为具有挑战性，原因在于存在混合不确定性——即认知不确定性（源于对模型参数的不完全认知）与偶然不确定性（反映固有生物变异性和随机环境条件）的结合。本研究提出一种贝叶斯模型更新（BMU）框架，用于校准近期提出的多物种生物膜生长模型。为实现混合不确定性下的高效推断，我们构建了基于时间分离随机力学（TSM）方法导出的降阶模型（ROM）。TSM方法能够高效传播偶然不确定性，从而实现单循环贝叶斯推断，避免了混合不确定性量化中通常需要的计算成本高昂的嵌套（双循环）方案。该BMU框架采用基于随机模型输出均值与方差构建的似然函数，即使在稀疏噪声数据下也能实现稳健的参数校准。我们通过两个案例研究验证了该方法：双物种与四物种生物膜模型。结果表明，我们的方法不仅能准确还原基础模型参数，还能提供与合成数据一致的预测响应。