Towards Scalable Gaussian Process Modeling

Numerous engineering problems of interest to the industry are often characterized by expensive black-box objective function evaluations. These objective functions could be physical experiments or computer simulations. Obtaining a comprehensive idea of the problem and/or performing subsequent optimizations generally requires hundreds of thousands of evaluations of the objective function which is most often a practically unachievable task. Gaussian Process (GP) surrogate modeling replaces the expensive function with a cheap-to-evaluate data-driven probabilistic model. While the GP does not assume a functional form of the problem, it is defined by a set of parameters, called hyper-parameters, that need to be learned from the data. The hyperparameters define the characteristics of the objective function, such as smoothness, magnitude, periodicity, etc. Accurately estimating these hyperparameters is a key ingredient in developing a reliable and generalizable surrogate model. Markov chain Monte Carlo (MCMC) is a ubiquitously used Bayesian method to estimate these hyperparameters. At GEs Global Research Center, a customized industry-strength Bayesian hybrid modeling framework utilizing the GP, called GEBHM, has been employed and validated over many years. GEBHM is very effective on problems of small and medium size, typically less than 1000 training points. However, the GP does not scale well in time with a growing dataset and problem dimensionality which can be a major impediment in such problems. For some challenging industry applications, the predictive capability of the GP is required but each second during the training of the GP costs thousands of dollars. In this work, we apply a scalable MCMC-based methodology enabling the modeling of large-scale industry problems. Towards this, we extend and implement in GEBHM an Adaptive Sequential Monte Carlo (ASMC) methodology for training the GP. This implementation saves computational time (especially for large-scale problems) while not sacrificing predictability over the current MCMC implementation. We demonstrate the effectiveness and accuracy of GEBHM with ASMC on four mathematical problems and on two challenging industry applications of varying complexity.