Application of physics-informed neural networks to predict concentration profiles in gradient liquid chromatography

Chromatography is one of the key methods in the analysis of mixture compositions, in the testing of chemical purity, as well as in the production of highly pure compounds. For this reason, it finds an important place in many industries. Currently, one of the most widely used techniques is gradient liquid chromatography (GLC), which offers improved elution ability of the analytes. Experimental determination of optimal separation parameters with GLC is tedious, hence various numerical methods are used to optimize these processes. Recently, Physics-Informed Neural Networks (PINNs) have emerged as an alternative to classical numerical methods since they can also serve as a tool for solving partial differential equations (PDEs). The main concept of the PINN, apart from the ability to detect hidden and complex relationships between variables through machine learning, is to reach consistency with the governing physical laws by using a loss function that takes PDEs into account, which allows to obtain the results with better accuracy. In the paper, two PINN models are proposed, based on datasets obtained from numerical solutions of the equilibrium dispersive (ED) chromatography column model. After training and testing phases, the models are able to predict the concentration profiles under linear and nonlinear GLC conditions with more than satisfactory accuracy. The first model (model A1) was tested under linear GLC conditions, with variable inlet concentration or injection time, while the second model (model A2) was validated both under linear and nonlinear GLC modes and with variable axial dispersion and mass transport resistances.