Estimating Adsorption Isotherm Parameters in Chromatography via a Virtual Injection Promoting Feed-forward Neural Network

TL;DR

This paper introduces VIP-FNN, a neural network-based method that uses synthetic data from physics models to improve the estimation of adsorption isotherms in chromatography, overcoming limitations of traditional inverse problem approaches.

Contribution

The paper presents a novel neural network approach, VIP-FNN, which leverages synthetic injection data to enhance adsorption isotherm estimation in chromatography.

Findings

VIP-FNN is efficient and robust in numerical experiments.

The method outperforms traditional regularization techniques.

It effectively handles limited and noisy experimental data.

Abstract

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the small noise in the measured response can lead to a large fluctuation in the estimated quantity of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method -- the Virtual Injection Promoting Feed-forward Neural Network (VIP-FNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model -- a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-FNN is an efficient and robust algorithm.