Interpretable Hybrid Machine Learning for Predicting Microbial Growth Curves: Comparing Direct Data-Driven, Two-Step Hybrid, and One-Step Hybrid Approaches

Predictive microbiology relies on a two-step workflow in which a primary model is fitted to each growth curve and secondary models relate the kinetic parameters to environmental conditions, which can propagate primary-fit uncertainty. This study compared three strategies for predicting Escherichia coli growth from temperature, pH, and water activity: (i) direct machine learning (ML) prediction of log counts; (ii) a two-step hybrid approach, in which modified Gompertz parameters estimated for each curve were mapped to environmental conditions by a neural network; and (iii) a one-step hybrid approach, in which the network predicted Gompertz parameters and was trained end-to-end on the growth-curve misfit. The 396 ComBase growth curves (4082 observations) were evaluated by repeated five-fold cross-validation grouped by environmental condition. Direct ML achieved an RMSE of 0.690 ± 0.085 log CFU/mL but yielded no kinetic parameters. The one-step approach was statistically equivalent to direct ML (RMSE = 0.712 ± 0.075; margin ±0.1 log CFU/mL), whereas the two-step approach was slightly less accurate (RMSE = 0.745 ± 0.101). The one-step model’s lag times and maximum growth rates agreed with independent primary-fit estimates (Spearman ρ = 0.89 and 0.93). Within the studied conditions, it offered the most favourable balance between accuracy and interpretability.