Uniform. design is a widely used space-filling approach for computer experiments, with its theoretical foundation rooted in the overall mean model and the Koksma-Hlawka inequality. The uniformity of design points is typically measured by discrepancies, among which the centered L2-discrepancy is the most popular one. However, the centered L2-discrepancy suffers severely from the curse of dimensionality in high-dimensional settings, leading to misleading evaluations of uniformity. To address this limitation, this paper systematically studies the weighted symmetric centered discrepancy (WSCD) . Introduced with weight parameters under the reproducing kernel framework, WSCD can be decomposed into the weighted sum of projection discrepancies of each sub-dimension. A method for selecting weight parameters is proposed for the weighted symmetric centered discrepancy, which makes the contribution rate of sub-projection discrepancies within three dimensions account for more than 90% of the total discrepancy. Accordingly, the discrepancy can effectively attach importance to the uniformity of low-dimensional projections in accordance with the effect hierarchy principle. Numerical experiments adopting the Morris function as the true model and the Gaussian process model as the prediction model show that the prediction mean square error of the optimal design based on the weighted symmetric centered discrepancy with optimized weights is significantly lower than that of the centered discrepancy and other commonly used discrepancies. This verifies that the new criterion possesses superior properties in evaluating uniformity.
