Integrating Order-of-Magnitude Analysis to Physics-Informed Neural Networks for Linear Chromatographic Models

A hybrid (gray-box) modeling framework, physics-informed neural networks (PINNs), has garnered significant attention. However, a huge challenge in applying PINNs to bioprocesses is developing a loss function that synergizes different bioprocess dynamics. To mitigate this challenge, a novel physics-based deep learning method was developed by integrating order-of-magnitude analysis to the loss function of PINNs (oPINNs) using biological first principles. Compared to standard PINNs and numerical methods for solving the forward problem of linear chromatographic models, oPINNs demonstrated notable improvements: an order-of-magnitude enhancement in accuracy with an equivalent sample size, or a 32-fold reduction in sample size for equivalent accuracy, along with a 1000-fold acceleration in computational speed for millisecond-scale simulation. Moreover, oPINNs showed exceptional robustness in weight determination and hyperparameter selection amidst variations in chromatographic model parameters. In summary, oPINNs represent a significant advancement in integrating physics-based deep learning into hybrid modeling of bioprocesses, particularly for developing real-time digital twins.