Robust Application of Bayesian Neural Networks to Equilibrium Dispersive Model of Chromatography Using Monte Carlo Simulations

Abstract

This article explores a data-driven methodology for investigating a one-dimensional equilibrium dispersive model of chromatography using a Bayesian regularized neural network. The model deliberates four key physicochemical factors: interstitial velocity, injected mass, diffusion coefficient, and retardation factor. To address ambiguity, Monte Carlo simulations are used to sample realistic parameter distributions and iteratively solve the model, improving extrapolative reliability, enabling probabilistic characterization, and sensitivity analysis. Within the Bayesian framework, Monte Carlo methods estimate the posterior predictive distribution, allowing the neural network to remain robust and quantify uncertainty under limited or noisy data. We compared the analytical solution with the Bayesian neural network solution by varying the four key factors. Strong graphical agreement was observed, and confirmatory consistency between both approaches. Lower diffusion coefficients produced sharper peaks, whereas higher diffusion led to smoother, more diffuse profiles. Similarly, higher velocities shortened the solute’s residence time, while lower velocities delayed elution. Both methods also showed agreement for different injected masses, with graphical and numerical results matching very closely. Finally, varying the retardation factor provided insight into solute–stationary phase interactions, with excellent agreement between analytical and neural network solutions. These results authenticate the reliability and precision of the Bayesian neural network in modeling chromatographic behavior.