Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model

TL;DR

This paper introduces a Bayesian ensemble of trees as a surrogate model for complex computer simulators, effectively identifying global minima especially in nonstationary or abrupt response scenarios, demonstrated through various examples including tidal power.

Contribution

It proposes a novel Bayesian ensemble of trees for computer experiments, enhancing global minimum estimation in challenging nonstationary simulators.

Findings

Effective in nonstationary and abrupt response scenarios

Improves global minimum estimation accuracy

Demonstrated with tidal power application

Abstract

In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by "surrogate models" such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the Expected Improvement criterion (Jones et al. 1998), we show that this ensemble is particularly effective when the simulator is ill-behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application.