Physics-informed neural networks to solve lumped kinetic model for chromatography process.

Numerical method is widely used for solving the mechanistic models of chromatography process, but it is time-consuming and hard to response in real-time. Physics-informed neural network (PINN) as an emerging technology combines the structure of neural network with physics laws, and is getting noticed for solving physics problems with a balanced accuracy and calculation speed. In this research, a proof-of-concept study was carried out to apply PINN to chromatography process simulation. The PINN model structure was designed for the lumped kinetic model (LKM) with all LKM parameters. The PINN structure, training data and model complexity were optimized, and an optimal mode was obtained by adopting an in-series structure with a nonuniform training data set focusing on the breakthrough transition region. A PINN for LKM (LKM-PINN) consisting of four neural networks, 12 layers and 606 neurons was then used for the simulation of breakthrough curves of chromatography processes. The LKM parameters were estimated with two breakthrough curves and used to infer the breakthrough curves at different residence times, loading concentrations and column sizes. The results were comparable to that obtained with numerical methods. With the same raw data and constraints, the average fitting error for LKM-PINN model was 0.075, which was 0.081 for numerical method. With the same initial guess, the LKM-PINN model took 160 s to complete the fitting, while the numerical method took 7 to 72 min, depending on the fitting settings. The fitting speed of LKM-PINN model was further improved to 30 s with random initial guess. Thus, the LKM-PINN model developed in this study is capable to be applied to real-time simulation for digital twin.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.