Physics-Informed Neural Networks for Liquid Chromatography

Liquid chromatography is a technique used to separate and purify components of a mixture. The method is frequently used in the biomedicine industry and life science to discover and develop new drugs. Here liquid chromatography can separate the drug candidate from its byproducts. For this, it is essential to achieve high purity to satisfy the requirements for biopharmaceutical drugs. However, the calculations for receiving optimal settings to achieve high purity are often computationally demanding. Thus the biomedicine industry would benefit from more efficient methods for obtaining optimal settings for the specific application. The problem involves solving a system of coupled PDEs which is typically done with numerical methods. Since numerical methods quickly become computationally demanding when increasing the grid size, this thesis focuses on investigating the opportunity to introduce Physics-Informed Neural Networks (PINNs) for solving PDEs in liquid chromatography fast and accurately. The methodology developed two PINNs, one where a network is trained to solve the PDEs for one unique parametrization and another where a PINN is trained to solve the PDEs for any parameterization of the PDEs. We show that PINNs can be trained to become the solution for one parametrization of the related PDEs, with a relative error of 0.60%. Moreover, the results demonstrate that a PINN can predict the solution with an average relative error of 1.53% for any parameterization. Furthermore, we show that this PINN can produce solutions at smaller regions of the solution domain 23 times faster than the numerical solver used for simulating ground truth data. The results give a great insight into how PINNs can be used in liquid chromatography applications and can be seen as a first step in introducing PINNs in liquid chromatography.