Figure 3
From: A Kriging-Based Approach to Autonomous Experimentation with Applications to X-Ray Scattering
Example of an error function used within the Kriging method. The error function drops to zero at locations where measurements have already been conducted. Measurement errors can be included in the Kriging error, but are commonly neglected for simplicity. If errors are included, the error function will not drop to zero but to the specified variance value of the particular measurement. Between the data points, the function exhibits low curvature ridges and plateaus. In the early stages of autonomous experiments, where there are few data points, maxima are mostly found along the boundary of the domain. These maxima do not generally satisfy the first necessary criterion for optima \((\frac{\partial {\sigma }^{2}}{\partial {\bf{p}}}=0)\). In later stages of an autonomous experiment, maxima will be found inside the domain but curvatures will often be small, which makes derivative-based optimization methods inefficient. Global optimization, however, allows for an efficient optimization for this class of functions over bounded, low-dimensional (<30) sets. In the example shown here, the next measurement will take place at \([20,40]\) (marked).
