Abstract

Adsorption systems are characterized by challenging behavior to simulate any numerical method. A novel field of study emerged within the numerical method in the last two years: the physics-informed neural network (PINNs), the application of artificial intelligence to solve partial differential equations. This is a complete new standpoint for solving engineering first-principle models, which up to that date was not explored in the field of adsorption systems. Therefore, this work proposed the evaluation of PINN to address the numerical solutions of a fixed-bed column where a monoclonal antibody is purified. The PINNs solution is compared with a traditional numerical method. The results show the accuracy of the proposed PINNs when compared with the numerical method. This points towards the potential of this technique to address complex numerical problems found in chemical engineering.

Highlights

  • Introduction published maps and institutional affilSolving partial differential equation (PDE) systems is crucial in several fields

  • We study the peculiarities of these systems from the point of view of physics-informed neural networks

  • This work presents one of the first attempts to solve numerical problems arising from adsorption models with physics-informed neural networks

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Summary

Introduction

Solving partial differential equation (PDE) systems is crucial in several fields. The PDEs are essential within engineering, ranging from civil engineering to chemical engineering. They are responsible for the mathematical representation of the observed reality through time and space. The more complex the relationship of the observed phenomena throughout these two dimensions, the more complicated the PDE systems are, and the more difficult it is to obtain their solution. Following the nature of the PDEs, one can choose a myriad of options to obtain a numerical solution, ranging from the orthogonal colocation into finite elements to finite elements coped with RungeKutta. The numerical method is a consolidated field providing essential tools for engineers for several years. In 2019, this field started to be revolutionized by the advent of physics-informed neural networks (PINN) [1,2]

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