Scalable Fully Bayesian Gaussian Process Modeling and Calibration With Adaptive Sequential Monte Carlo for Industrial Applications

Abstract

Gaussian process (GP) regression or kriging has been extensively applied in the engineering literature for the purposes of building a cheap-to-evaluate surrogate, within the contexts of multi-fidelity modeling, model calibration, and design optimization. With the ongoing automation of manufacturing and industrial practices as a part of Industry 4.0, there has been a greater need for advancing GP regression techniques to handle challenges such as high input dimensionality, data paucity or big data problems, these consist primarily of proposing efficient design of experiments, optimal data acquisition strategies, sparsifying covariance kernels, and other mathematical tricks. In this work, our attention is focused on the challenges of efficiently training a GP model, which, to the authors opinion, has attracted very little attention and is to-date poorly addressed. The performance of widely used training approaches such as maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) sampling can deteriorate significantly in high-dimensional and big data problems and can lead to cost deficient implementations of critical importance to many industrial applications. Here, we compare an Adaptive Sequential Monte Carlo (ASMC) sampling algorithm to classic MCMC sampling strategies and we demonstrate the effectiveness of our implementation on several mathematical problems and challenging industry applications of varying complexity. The computational time savings of the ASMC approach manifest in large-scale problems helping us to push the boundaries of applicability and scalability of GPs for model calibration in various domains of the industry, including but not limited to design automation, design engineering, smart manufacturing, predictive maintenance, and supply chain manufacturing.