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

2025-12-17

AI Summary

Modeling multispecies bacterial biofilm growth is challenged by parameter calibration under hybrid uncertainty (epistemic and aleatory). This paper proposes a reduced-order surrogate model based on time-scale separation stochastic mechanics (TSM), marking the first application of TSM to construct computationally efficient surrogates enabling single-loop Bayesian updating—thereby overcoming the prohibitive computational cost of conventional double-loop approaches. We further design a joint mean–variance likelihood function to enhance robustness in calibrating sparse, noisy data. In benchmark cases involving two- and four-species biofilms, the method accurately infers constitutive parameters and yields predictions highly consistent with synthetic ground-truth data. Computational efficiency is markedly superior to double-loop methods. The framework establishes a new paradigm for uncertainty quantification and rapid Bayesian inference in complex biofilm systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Calibrates biofilm growth model parameters under hybrid uncertainties.
• Uses Bayesian updating with a surrogate model for efficient inference.
• Handles epistemic and aleatory uncertainties in sparse, noisy data.

Innovation

• Bayesian model updating for parameter calibration
• Time-Separated Stochastic Mechanics for efficient uncertainty propagation
• Single-loop inference to avoid computationally expensive nested schemes