Real‑Time Model Predictive Control of Monoclonal Antibody Capture in Continuous Manufacturing Using Physics‑Informed Neural Networks Accelerated Mechanistic Modeling

Continuous bioprocessing with Protein A affinity chromatography has demonstrated great potential to increase productivity and reduce the cost of goods in monoclonal antibody (mAb) production. However, maintaining process stability and responding to dynamic changes remains significant challenges, particularly in the real-time optimization and control of multi-column periodic counter-current chromatography (PCC) for Protein A affinity chromatography, due to the computational complexity of rapidly solving mechanistic models. To address this challenge, this study developed distilled physics-informed neural networks (PINNs) based on the general rate model (GRM) to accelerate and enhance the breakthrough curve fitting and four-column PCC (4C-PCC) process optimization. The distilled PINNs achieved a balance between prediction accuracy and computational speed. The 157k-parameter distilled PINN enabled the breakthrough curve fitting and 4C-PCC process optimization approximately 10 times faster than numerical methods while improving accuracy by about 40%. A smaller 2k-parameter model achieved a 22-fold acceleration with an acceptable trade-off in accuracy, and the optimization time was reduced to 1.44 s. Explainability analyses confirmed the PINN's capability to capture nonlinear and interactive effects among key process parameters. The PINN-accelerated GRM was then integrated with real-time model predictive control (MPC) and applied to a lab-scale continuous manufacturing process. PINN-based MPC maintained robust control of binding capacity and yield, achieving a productivity of 35 g/L resin/h and resin capacity utilization of 90%, despite resin capacity decay and upstream variability. This work demonstrates that the PINNs can provide a computationally efficient and physically consistent framework for real-time optimization and control of continuous processes. Integrating a mechanistic model with neural networks can enhance process understanding and robustness, supporting the implementation of continuous biomanufacturing for therapeutic proteins.