Data-Efficient Convex Hybrid Modeling for Reliable Bioreactor Scale-Up Under Sparse Calibration Data

Reliable bioreactor scale-up remains a major challenge in process engineering because microbial kinetic parameters often change nonlinearly across reactor volumes as a result of mixing heterogeneity, oxygen-transfer limitations, and regime-dependent hydrodynamic effects. Conventional power-law or logarithmic scale-up correlations are simple and practical, but they may produce biased extrapolations when applied beyond the calibration range. This work presents a data-efficient convex hybrid modeling framework for predicting scale-dependent bioprocess kinetics under sparse experimental conditions. The approach combines competing empirical and mechanistically inspired scaling hypotheses under simplex-constrained weights, allowing the model to preserve physical plausibility while identifying the dominant scale-transfer regime from limited data. Using a published lipase fermentation case study spanning laboratory, pilot, and industrial bioreactor scales, sigmoidal kinetic parameters were first extracted using Logistic, Gompertz, and Baranyi–Roberts models. These parameters were then extrapolated through hybrid combinations of power-law, logarithmic, piecewise log-linear, and monotonic mechanistic surrogate relations. The resulting framework improved industrial-scale prediction accuracy compared with single-law scaling and unconstrained regression baselines, while requiring only a small number of calibration scales. In addition, incremental weight-stabilization analysis showed that convex hybrid weights can converge toward statistically stable structural configurations as additional observations are incorporated, providing a quantitative indicator of minimum data requirements for reliable inference. These results demonstrate that convex hybrid scale-up modeling offers an interpretable, computationally efficient, and experimentally economical strategy for robust process extrapolation. The proposed framework is potentially transferable to other microbial and biochemical processes where full-scale experimentation, dense pilot campaigns, or high-fidelity computational fluid dynamics simulations are impractical.