Mechanistically Constrained Multi-Fidelity Scaling Enables Accurate 100 m³ Fermentation Predictions from Only Three Calibration Volumes

Accurate extrapolation in data-scarce scientific systems remains a central challenge for machine intelligence. In microbial bioprocessing, kinetic parameters change non-monotonically with reactor volume due to interacting hydrodynamic, oxygen-transfer, and mixing effects, rendering classical empirical scaling laws unreliable. Here, we introduce a mechanistically constrained multi-fidelity learning framework that reconstructs the full four-dimensional Baranyi–Roberts kinetic parameter space using only three small-scale datasets (10 L, 100 L, 4 m³), without access to the industrial 100 m³ reactor data during model training or weight inference. The method represents scale dependence as a convex combination of four structural hypotheses: power-law, logarithmic, piecewise log-linear, and a mechanistic CFD-inspired surrogate, and infers weights via a convex optimization that enforces physical monotonicity. The learned model assigns >98% weight to the piecewise log-linear basis, revealing a latent regime transition between 100 L and 4 m³. When propagated through the growth model, the hybrid prediction accurately recovers the full 100 m³ biomass trajectory (RMSE = 1.796 g·L⁻¹), approaching the accuracy of a direct fit (0.749 g·L⁻¹), while four standard machine-learning baselines fail under extrapolation by factors of 5 to 25 times. These results establish a data-efficient, interpretable workflow for extrapolative prediction across scales.

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