Data-efficient hybrid parameter scaling for accurate microbial bioreactor scale-up.

Accurately predicting microbial fermentation performance at an industrial scale is challenging due to hydrodynamic and oxygen-transfer limitations, which disrupt geometric similarity and cause nonlinear changes in apparent production kinetics. The goal of this work is to develop a data-efficient hybrid scaling law that extrapolates time-course model parameters of relative lipase concentration across bioreactor volumes using minimal experimental scales. Sigmoidal lipase accumulation curves from 10 L, 100 L, 4 m³, and 100 m³ bioreactors were extracted from the study of Geraats (1994) and fitted using Logistic, Gompertz, and Baranyi–Roberts (BR) models. Kinetic parameters (Lmax, k or µ, tmid or λ) obtained from small-scale bioreactors (10 L and 100 L) were used to construct two minimal two-point relations: power-law and logarithmic. As these relations showed systematic overshoot and undershoot during extrapolation, a hybrid convex-weighting scheme was developed and calibrated at the 4 m³ pilot scale. When applied to the 100 m³ industrial dataset, the hybrid method significantly improved prediction accuracy compared to either scaling law alone, reducing RMSE by more than 60%. The Baranyi–Roberts model combined with hybrid scaling achieved the highest overall accuracy (RMSE = 2.651). Requiring only three experimental scales, this approach is computationally efficient, mechanistically interpretable, and suitable for industrial contexts where extensive pilot campaigns or computational fluid dynamics simulations are not feasible. The hybrid scaling framework thus offers a practical and data-efficient solution for reliable bioreactor scale-up.