Response surface methodology using Gaussian processes: Towards optimizing the trans-stilbene epoxidation over Co2+–NaX catalysts

Bayesian variable selection for Gaussian process regression: Application to chemometric calibration of spectrometers

“…Empirical comparative studies have confirmed the outstanding performance of Gaussian process regression with respect to other non-linear models [11,12,13]. As a result, Gaussian process models have been widely applied to various problems in statistics and engineering [14,11,15,16,17,18,13].…”

“…θ j (t + ) = θ j (t) + p j t + 2 (17) p j (t + ) = p j (t + 2 ) − 2 ∂E ∂θ j (θ(t + )) (18) where t is the virtual time for the dynamic system, is the step size for discretizing the dynamic system. Note that the definition of E results in the following expression for the above derivative terms:…”

Interpretation of non-linear empirical data-based process models using global sensitivity analysis

“…logarithmic or logistic) transformation is particularly attractive if it is known a priori to result in linear factor-response relationship, and thus linear regression can be used. However in general situation, the prediction accuracy of the polynomial regression is unsatisfactory if the chemical process is complex and does not conform to the restrictive functional form [6,7,8,9]. Consequently, the model-based process understanding and optimization may be unreliable .…”

Model-aided optimization and analysis of multi-component catalysts: Application to selective hydrogenation of cinnamaldehyde

“…To obtain better performance, the prediction mean and variance should be jointly considered, since the variance indicates the lack of exploration of the region and the need for more experiments. In the literature, several methods have been investigated to handle prediction variance, including maximization of lower or upper prediction bound (Yuan et al, 2008;Tang et al, 2010), minimization of information free energy (Lin and Jang, 1998), maximization of relative information gain (Coleman and Block, 2007), and maximization of expected improvement (EI) (Jones, 2001). Among these methods, EI is based on a rigorous statistical formulation and does not require 6 user-determined weights as other methods do.…”

“…With limited data, model-aided local sensitivity analysis (SA) has been widely used for this purpose (Tang et al, 2010;Yuan et al, 2008). Mathematically, SA studies how the variation in the factors (x = [x 1 , .…”