Gaussian Process Regression Modeling Benchmark of Atomic Vacancy Concentrations in Solder Bumps

Abstract

Expensive and scarce design objective data is an increasingly relevant problem in modern engineering applications. Gaussian process regression is a popular method that tackles this challenge by efficiently performing response surface surrogate modeling across a global design space. However, practitioners of this modeling procedure often fail to adequately tailor the regression model to the data. This work aims to address this issue by considering a variety of covariance kernels and fixed or learnable noise values. We demonstrate the efficacy of this consideration by means of both a synthetic design problem and a real-life micro-electronic design problem. This problem requires a surrogate model of the atomic vacancy concentration within a solder bump structure. Calculating this concentration relies on expensive thermo-mechanical finite element simulations. Previously, the commercial data-driven pipeline package Optimus has been used to build a Gaussian process regression model. However, using GPyTorch, we can vary surrogate modeling choices to obtain a model that more effectively generalizes to the entire design space. This process is not much more time-consuming than cross-validated Gaussian process regression with Optimus, taking only 0.31% of the time needed to sample the design space. This shows that careful selection of response surface modeling hyperparameters is both non-trivial and effective when constructing an efficient and reliable surrogate model.