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.

翻译：补料分批培养是利用哺乳动物细胞生产生物制品的成熟操作模式。定量建模整合了关键反应步骤的动力学与基于通量平衡分析的最优驱动代谢通量分配，但已知这种方法会导致某些数学不一致性。本文提出一种物理信息驱动的数据驱动混合模型（"灰箱"模型），从过程数据中学习中国仓鼠卵巢（CHO）细胞生物反应器的动态演化模型。该方法融合了物理定律（如质量平衡）与代谢通量的动力学表达式。机器学习（ML）被用于：（a）直接学习演化方程（黑箱建模）；（b）恢复未知物理参数（"白箱"参数拟合），或——关键之处——（c）学习部分未知的动力学表达式（灰箱建模）。我们将超定代谢生物物理系统的凸优化步骤编码为可微前馈层嵌入网络架构，从而将部分物理知识与数据驱动机器学习相连接。