Machine-learning surrogates enable rapid prediction of 3-D substrate gradients in industrial bioreactors

Abstract High-fidelity computational fluid dynamics (CFD) provide detailed substrate gradient predictions in industrial stirred-tank bioreactors but are computationally intensive, limiting their routine application. We developed surrogate models trained on $$760$$ 760 CFD simulations to rapidly predict fully 3-D substrate concentration fields from global operating conditions (e.g., stirring speed, feeding strategy, feeding point location, fluid density and viscosity, liquid height, bio-kinetic parameters, biomass concentration), and local spatial descriptors (e.g., distance to the feeding point). Among various methods, attention-based neural networks achieved the highest accuracy (test $${{{\rm{R}}}}^{2}\approx 0.91$$ R 2 ≈ 0.91 ), capturing essential mixing features and enabling millisecond-scale inference—up to a million-fold speed-up compared to CFD. These surrogates facilitate rapid exploration of operating spaces, supporting real-time optimization and digital-twin frameworks in bioprocessing. Our results demonstrate that data-driven models can effectively couple hydrodynamics and biokinetics to provide fast, accurate spatial predictions, advancing capabilities for industrial bioreactor design and control.