Application of Physics-Informed Neural Network in prediction of chromatographic concentration profiles Filip Rękas1, Marcin Chutkowski2, Krzysztof Kaczmarski2 1 Doctoral School of the Rzeszów University of Technology, Poland 2 Rzeszow University of Technology, Poland The Physics-Informed Neural Network is an emerging technique that has been used for solving various problems involving partial differential equations (PDE). The main concept of the PINN is to reach consistency with the governing physical laws by using training loss function that takes PDEs into account and allows to obtain the results with better accuracy. In this work application of the PINN method to predict the gradient elution profiles of single-component and a binary mixture systems is presented. The dataset for training and testing the PINN was collected by solving the ED column model using the volume method. The following dimensionless form of the Equilibrium Dispersive Model is considered: ௧ ௧ ௘ ௧ ௘ ௧ ଶ ଶ with ௙ ᇱ ௙for ௣ and ௙ ᇱ for ௣ The dimensionless parameters were defined as follows: ௭ ௅ ௧௨ ௅ఌ೐ y ஼ ஼ೝ ௤ ஼ೝ ௦ ௤ೞ ௖ೝ ௨௅ ஽ಽఌ೐ where cr was assumed to be equal to 1 and L is - column length. A scheme of the PINN architecture was illustrated in Fig. 1, where the three input neurons, corresponding to spatiotemporal coordinates (x, ) and injection features ( ) were placed. The injection features are the inlet concentration ( ଴) and the time during the constant concentration is fed into the column ( ௣). On the other hand, the outputs are spatiotemporal fluid-phase concentrations contained in the pores, y(x, ), and concentration in the stationary phase, Q(x, ), which is similar to that proposed by Subraveti et al. [1]. The given outputs are subsequently fed into automatic differentiation layer, which computes partial derivatives. Obtained PDE loss ( ௉஽ா) is further factored into the total loss ( ). Fig. 1 The sketch of Physics-Informed Neural Network structure. INTRODUCTION RESULTS AND DISCUSSION CONCLUSIONS Presented model was implemented in PyTorch framework with the Adam optimizer as the gradient descent based algorithm. The weights were initialized by the Glorot initialization. The fully-connected neural network was made up of 5 hidden layers with 50 neurons in each. Latin hypercube sampling (LHS) was employed to determine the collocation points. To cover the spatiotemporal domain, the number of collocation points was set to 5000. The Hyperbolic tangent was utilized as the activation function. The following formula for the loss function has been proposed: ௉஽ா ூ஼ ஻஼ where corresponds to trainable parameters, in turn ௉஽ாdenotes: ௉஽ா ௙ ௧ ௧ ௘ ௧ ௘ ௧ ଶ ଶ ଶ ே೑ ௜ REFERENCES [1] Subraveti et al., Ind. Eng. Chem. Res. 2023, 62, 5929−5944. Fig. 5 Case study for various injection time: comparison of the PINN predicted and the ED model solution. Fig. 2 Case study for various inlet concentrations: comparison of the PINN predicted and the ED model solution: a) single-compound system, b) binary mixture system. Fig. 3 Case study for various injection time: comparison of the PINN predicted and the ED model solution: a) single-compound system, b) binary mixture system. Fig. 4 Case study for various tg: comparison of the PINN predicted and the ED model solution. a) single-compound system, b) binary mixture system. ACKNOWLEDGMENT This work is supported by: Grant NCN 2022/45/B/ST8/00591 “Analytical and preparative gradient chromatography – advanced modeling” from the Polish National Science Centre The presented concept of using the PINN to predict gradient elution profiles is novel and previously unreported. The effectiveness of the PINN's prediction of elution curves has been verified by comparing them with ED model solutions. The optimization of the efficiency of species separation can be a tedious task that often requires up to several thousand model solutions. It seems that the solution of this problem may be the application of the physics-informed neural networks. Future work