Comparative Analysis of Gaussian Process Regression, Richards Model, and Polynomial Regression for Modeling Bacterial Growth Dynamics of Proteus Mirabilis

Modeling bacterial growth dynamics is crucial for understanding microbial behavior in various applica tions, including microbiology, medicine, and food safety. This study compares three modeling approaches Gaussian Process Regression (GPR), Richards Model, and Polynomial Regression (PR) to evaluate their effectiveness in predicting bacterial growth patterns. The models were assessed based on their ability to estimate key growth parameters, including lag time (tlag), maximum specific growth rate (µmax) as well as their predictive accuracy using Mean Squared Error (MSE) and (R2) values. The results indicate that the Richards model provides strong biological interpretability, explicitly capturing bacterial growth phases, whereas GPR excels in handling noisy data and offering probabilistic predictions with confidence inter vals. In contrast, PR, while computationally efficient, struggles with asymptotic behavior and is sensitive to noise. The study concludes that GPR is ideal for noisy datasets requiring uncertainty quantification, while the Richards model is more suitable for structured data with well-defined growth trends. Combining these models can provide a more comprehensive understanding of bacterial growth, optimizing predic tions across various experimental conditions.