Hybrid modeling framework for bioprocesses with minimal prior knowledge and limited data

Hybrid models that couple mechanistic ordinary differential equations (ODEs) with neural networks are increasingly used in bioprocess engineering, yet most published approaches assume either substantial prior knowledge or relatively large datasets. This work proposes a hybrid modeling framework for early-stage bioprocess development, where only a few batch experiments are available and standard artificial intelligence (AI) techniques are difficult to apply. The mechanistic structure is constructed using only qualitative, widely accepted biological constraints (e.g., non-negativity, zero-invariance, and biomass-mediated interactions), while unknown functional dependencies are learned by a feedforward neural network embedded in the ODE right-hand side. To exploit the natural organization of batch data, we introduce a minibatch training strategy in which each minibatch corresponds to one entire batch experiment, combined with regularization to mitigate overfitting. We demonstrate the approach on (i) synthetic Escherichia coli growth with overflow metabolism and (ii) experimental astaxanthin production by Xanthophyllomyces dendrorhous. In both cases, models trained from as few as three batch experiments accurately predict an unseen validation batch and the learned neural components recover biologically consistent patterns. Thus, the framework contributes to AI by enabling constrained neural differential models that learn interpretable dynamics from limited, structured data, with applications to early-stage bioprocess engineering.