Tree-Based Sequential Sampling for Efficient Designs in Package Electrical Analysis

The use of surrogate models (SMs) has become popular in electromagnetic (EM) design and optimization. Traditional SMs, while beneficial, are often hindered by the inherent complexity and nonlinearity of EM systems, leading to challenges in data representation and design space exploration. Addressing these challenges, we introduce a novel tree-based learning strategy for sampling within high-dimensional EM design spaces. Our method emphasizes the localized exploration to accurately capture the unique output behaviors at various frequencies in multi-frequency EM simulations. The proposed method focuses on refining the sampling process instead of optimizing an objective function. The resulting strategy is a robust, nonparametric learning approach that facilitates the sequential selection of design configurations, promoting uniform accuracy in the sampled data. It also enhances the interpretability in high-dimensional spaces and provides a variable importance measure for output profile discrimination. Our empirical results show that this strategy improves the learning trajectory of SMs against random sampling from a Latin hypercube design.