Sequential Design for Computer Experiments with a Flexible Bayesian Additive Model
This addresses the challenge of optimizing complex, costly simulations in fields like engineering, though it is incremental as it builds on existing Bayesian and ensemble methods.
The paper tackled the problem of efficiently estimating the global minimum of expensive computer simulators by proposing a new surrogate model based on a Bayesian ensemble of trees, showing it is particularly effective for ill-behaved simulators with nonstationarity or abrupt changes, as illustrated in applications like tidal power.
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.