Physics-informed neural network modeling of purple non-sulfur bacteria growth and pH dynamics under varying light conditions

Upcycling residual streams generated by agri-food industries offers a promising strategy to reduce their environmental impact. In this context, biological conversion using purple non-sulfur bacteria (PNSB) is an attractive approach for valorizing organic residues. However, their dynamic modeling is still a recent area of interest, presenting numerous challenges related to observed behavior and sensitivity to operating conditions. This work investigated the dynamic modeling of PNSB growth cultivated on molasses under varying light intensities. A mechanistic model is first developed to predict biomass growth and carbon source consumption, while explicitly describing pH dynamics. The model (and its variants) is subsequently exploited under the paradigm of physics-informed neural networks (PINNs), and different PINN structures with varying levels of embedded physical knowledge are explored, including: (i) a PINN based on a physical model with explicit light intensity dependence, (ii) a PINN relying on a physical model without light dependence, (iii) a PINN trained combining structural physics with data-driven kinetics. In addition, a classical artificial neural network (ANN) trained with data augmentation is considered a purely data-driven benchmark. All approaches are evaluated for data fitting and predictive performance and compared with the proposed physical models. The results indicate that PINNs can improve predictive accuracy while preserving physical consistency, suggesting their potential for robust bioprocess modeling and as a basis for future control-oriented developments.