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Digital Twin Calibration for Biological System-of-Systems: Cell Culture Manufacturing Process

Fuqiang Cheng, Wei Xie, Hua Zheng

TL;DR

This work tackles calibrating a modular Bio-SoS digital twin for cell culture by developing a gradient-based sequential design of experiments that exploits mechanistic structure to achieve interpretable, sample-efficient learning. The method combines Maximum Likelihood Estimation with bootstrapping for parameter updates and uses Linear Noise Approximation plus Euler's method to propagate uncertainty and derive a surrogate gradient for policy optimization. Key contributions include a formal finite-horizon calibration framework, a mechanistic surrogate via LNA, and a gradient-based optimal learning algorithm that guides most informative data collection. Empirical validation on a CHO cell culture model demonstrates substantial improvements in prediction accuracy and parameter estimation efficiency over random and Gaussian Process-based baselines, with practical implications for faster, more reliable bioprocess optimization and digital twin deployment in biomanufacturing.

Abstract

Biomanufacturing innovation relies on an efficient Design of Experiments (DoEs) to optimize processes and product quality. Traditional DoE methods, ignoring the underlying bioprocessing mechanisms, often suffer from a lack of interpretability and sample efficiency. This limitation motivates us to create a new optimal learning approach for digital twin model calibration. In this study, we consider the cell culture process multi-scale mechanistic model, also known as Biological System-of-Systems (Bio-SoS). This model with a modular design, composed of sub-models, allows us to integrate data across various production processes. To calibrate the Bio-SoS digital twin, we evaluate the mean squared error of model prediction and develop a computational approach to quantify the impact of parameter estimation error of individual sub-models on the prediction accuracy of digital twin, which can guide sample-efficient and interpretable DoEs.

Digital Twin Calibration for Biological System-of-Systems: Cell Culture Manufacturing Process

TL;DR

This work tackles calibrating a modular Bio-SoS digital twin for cell culture by developing a gradient-based sequential design of experiments that exploits mechanistic structure to achieve interpretable, sample-efficient learning. The method combines Maximum Likelihood Estimation with bootstrapping for parameter updates and uses Linear Noise Approximation plus Euler's method to propagate uncertainty and derive a surrogate gradient for policy optimization. Key contributions include a formal finite-horizon calibration framework, a mechanistic surrogate via LNA, and a gradient-based optimal learning algorithm that guides most informative data collection. Empirical validation on a CHO cell culture model demonstrates substantial improvements in prediction accuracy and parameter estimation efficiency over random and Gaussian Process-based baselines, with practical implications for faster, more reliable bioprocess optimization and digital twin deployment in biomanufacturing.

Abstract

Biomanufacturing innovation relies on an efficient Design of Experiments (DoEs) to optimize processes and product quality. Traditional DoE methods, ignoring the underlying bioprocessing mechanisms, often suffer from a lack of interpretability and sample efficiency. This limitation motivates us to create a new optimal learning approach for digital twin model calibration. In this study, we consider the cell culture process multi-scale mechanistic model, also known as Biological System-of-Systems (Bio-SoS). This model with a modular design, composed of sub-models, allows us to integrate data across various production processes. To calibrate the Bio-SoS digital twin, we evaluate the mean squared error of model prediction and develop a computational approach to quantify the impact of parameter estimation error of individual sub-models on the prediction accuracy of digital twin, which can guide sample-efficient and interpretable DoEs.
Paper Structure (14 sections, 2 theorems, 29 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 14 sections, 2 theorems, 29 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Problem Description and Bio-SoS Mechanistic Model
  3. Single Cell Model
  4. Macro-Kinetic State Transition
  5. State Transition Probability
  6. Digital Twin Calibration for Bio-SoS Mechanistic Model
  7. Model Inference and Parameter Update
  8. Policy Gradient Estimation and Optimal Learning
  9. Linear Noise Approximation on Bio-SoS Dynamics
  10. First-Order Euler's Method for Solving LNA
  11. Empirical Study
  12. Cell Culture Model and Validation
  13. Digital Twin Calibration
  14. CONCLUSION

Key Result

Lemma 1

Conditioning on the current state $\pmb {s}_t$ and model parameter $\pmb\theta$, the state change during in any small time interval $(t, t + \Delta t]$ is $\Delta \pmb{s}_{t+1}=\pmb{s}_{t+1}-\pmb {s}_t$ following a multi-variate normal distribution $\mathcal{N}\{\pmb{\mu}(\pmb\theta), \Sigma(\pmb\th

Figures (5)

  • Figure 1: An illustration of the multi-scale mechanistic model for cell culture process and Bio-SoS.
  • Figure 2: The procedure illustration of the proposed calibration approach.
  • Figure 3: The cell culture mechanistic model was validated by using the experimental data. Red dots represent the experimental data from the literature, while the blue lines indicate the simulation predictions from our model, with the mean and 95% CI calculated from 20 replications.
  • Figure 4: mAb Prediction Error
  • Figure 5: Parameter Estimation Error

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof