Investigation into the ability of Gaussian processes to faithfully reconstruct Chromatographic Response Function surfaces.

To give guidance to future research on computer-aided method development, the present study aimed at quantifying the accuracy with which Gaussian processes can represent typical Chromatographic Response Function (CRF) surfaces underlying chromatographic method development. Gaussian processes make up the core of Bayesian optimization, an optimization method that currently shows great promise to solve chromatographic method development problems. CRF surfaces are known to be very complex and jagged, with many local minima and maxima. On the other hand, the Matérn-based kernels commonly used in Gaussian processes typically impose strong smoothness assumptions that conflict with sharp variations and many closely spaced local extrema. To obtain an unbiased assessment of the reconstruction accuracy, grid- and Bayesian optimization-based Gaussian process fittings were investigated. Both showed poor reconstruction of the complete CRF surface, even for relatively simple 10-component samples. This suggests a limited ability of the Gaussian process-based surrogate models making use of Matérn-based kernels to accurately capture the fine details of the CRF surfaces and delineate robustness regions. Grid-based approaches generally outperformed Bayesian optimization-based methods in terms of global reconstruction accuracy, while Bayesian optimization-based approaches were more successful at locating acceptable optima. However, both required substantially more experimental data points than conventional model-based strategies. Furthermore, for the most challenging scenario, in which "only" 25 evaluations were performed for a 20-component sample, the median difference with the true optimal method time ranged from 27% (10-component sample) to 102% (20-component sample), provided a correct solution was found.