  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 modelling); (b) recover unknown
physical parameters ("white-box" parameter fitting) or -- importantly -- (c)
learn partially unknown kinetic expressions (gray-box modelling). 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.
