A Sequential Weighted Laplacian Regularized Optimal Design for Response Surface Modeling of Expensive Functions with Outliers: An Application in Linear Elastic Fracture Mechanics

There are several sequential and adaptive strategies designed to reduce the number of experiments in Response Surface Methodology (RSM). However, most of the existing sequential and adaptive methods are sensitive to the existence of possible outliers. In this paper, we propose an active learning methodology based on the fundamental idea of adding a Laplacian penalty to the D-optimal design and integrate that with robust regression to look for the most informative settings to be measured, while reducing the influence of possible outliers. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces we extend the proposed methodology to Reproducing Kernel Hilbert space (RKHS). Through an extensive simulation study accompanied by a thorough sensitivity analysis, we show that the proposed framework outperforms traditional response surface methodology designs in the presence of outliers. We also conduct a study utilizing a hierarchical function used in linear elastic fracture mechanics to illustrate practicality of the proposed methodology.