Surrogate model for Bayesian optimal experimental design in chromatography

Abstract

We applied Bayesian Optimal Experimental Design (OED) in the estimation of parameters involved in the Equilibrium Dispersive Model for chromatography with two components with the Langmuir adsorption isotherm. The coefficients estimated were Henry's coefficients, the total absorption capacity and the number of theoretical plates, while the design variables were the injection time and the initial concentration. The Bayesian OED algorithm is based on nested Monte Carlo estimation, which becomes computationally challenging due to the simulation time of the PDE involved in the dispersive model. This complication was relaxed by introducing a surrogate model based on Piecewise Sparse Linear Interpolation. Using the surrogate model instead the original reduces significantly the simulation time and it approximates the solution of the PDE with high degree of accuracy. The estimation of the parameters over strategical design points provided by OED reduces the uncertainty in the estimation of parameters. Additionally, the Bayesian OED methodology indicates no improvements when increasing the number of measurements in temporal nodes above a threshold value.