A Physics-Informed Computational Framework for Forward Prediction and Inverse Closure Learning of Pore-Scale Biofilm Growth

<title>Abstract</title> <p> Modeling biofilm growth in porous media is a challenging multiphysics problem due to the complex coupling of flow, nutrient transport, and microbial kinetics across space and time. Motivated by the nutrient-regulated, non-monotonic (S-shaped) relationship between biomass and pore-scale biofilm expansion (growth and diffusion) revealed by time-resolved microfluidic imaging, we propose a modified density-dependent biofilm diffusion model for confined pore spaces with an effective self-inhibition term. Coupling this flow–transport–growth process model with microfluidic observations via a physics-informed neural network enables accurate predictions in farther-ahead extrapolation (R ² =0.93), outperforming both the calibrated numerical model (R ² =0.85) andthe purely data-driven model (R ² =0.86). The framework further enables inverse refinement of the observation-scale self-inhibition closure under coupled PDE constraints and improves agreement with experimental observations. Transfer learning also adapts the pre-trained model to a related kinetic scenario with sparse data. This study provides a data-efficient computational strategy for predictive simulation and inverse closure learning in coupled biofilm-mediated transport systems. </p>