In this work, we present a neural network-based model that predicts growth kinetics by incorporating multiple biochemical constraints into the loss function of the neural network, in particular material (carbon and nitrogen) balance and metabolic flux balance. These constraints effectively reduce the data requirements, narrow the solution spaces to biologically feasible solutions, and enhance interpretability. Additionally, it enables the inference of critical, yet often difficult-to-measure, bioprocess parameters such as gas consumption rates and biomass composition. We demonstrate the application of this approach through a case study on E. coli cell culture. Finally, we discuss potential extensions of this approach, emphasizing how the application of multiple biological constraints can serve as a foundation for a multilevel framework in AI-driven virtual cell models, enabling interpretable and biologically grounded predictions.