Fed-batch culture is an established operation mode for the production of biologics using mammalian cell cultures. Quantitative modeling integrates both kinetics for some key reaction steps and optimization-driven metabolic flux allocation, using flux balance analysis; this is known to lead to certain mathematical inconsistencies Here, we propose a physically-informed data-driven hybrid model (a “gray box”) to learn models of the dynamical evolution of Chinese Hamster Ovary (CHO) cell bioreactors from process data The approach incorporates physical laws (e.g. mass balances) as well as kinetic expressions for metabolic fluxes Machine learning (ML) is then used to (a) directly learn evolution equations (black-box modeling); (b) recover unknown physical parameters (“white-box” parameter fitting) or—importantly—(c) learn partially unknown kinetic expressions (gray-box modeling) We encode the convex optimization step of the overdetermined metabolic biophysical system as a differentiable, feed-forward layer into our architectures, connecting partial physical knowledge with data-driven machine learning