and the PCA scores, where PC1 captures the dominant trade-off (70% variance) and PC2 captures the remaining orthogonal variation (30%), enabling uncertainty-aware prediction and screening under practical data constraints. Figure 1: Scatterplot between calculated adsorption energies ( 1, 2), and removal of linear correlation using PCA. In Figure 2 (top), we show the 4D omnidirectional variogram of both principal components. To perform GPR, we need to specify a grid. Because we are in 4D, specifying a regular dense Cartesian grid would be costly; indeed, using 100 points in each dimension results in 1004 grid cells. Luckily, GPR can be performed on an irregular, data-adaptive grid. We draw m=50,000 query locations by perturbing each observed sample within a small bandwidth (0.15) and clipping to the variable bounds. This concentrates evaluation where data exist and avoids empty corners of the hypercube. Figure 2 (bottom) shows a 2-D projection (X1 vs. X3) of the 4-D query set (blue) overlaid with the observations (red). Because GPR predicts at arbitrary locations, this unstructured grid is valid and reduces computational cost by orders of magnitude while preserving resolution in the regions of interest.
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