Batch sequential designs for computer experiments

Abstract

Computer models simulating a physical process are used in many areas of science. Due to the complex nature of these codes it is often necessary to approximate the code, which is typically done using a Gaussian process. In many situations the number of code runs available to build the Guassian process approximation is limited. When the initial design is small or the underlying response surface is complicated this can lead to poor approximations of the code output. In order to improve the fit of the model, sequential design strategies must be employed. In this paper we introduce two simple distance based metrics that can be used to augment an initial design in a batch sequential manner. In addition we propose a sequential updating strategy to an orthogonal array based Latin hypercube sample. We show via various real and simulated examples that the distance metrics and the extension of the orthogonal array based Latin hypercubes work well in practice.

Sequential tuning of complex computer models

“…As far as we know, this is the first attempt to propose a sequential design for estimating tuning parameters of a computer model. [14][15][16][17][18][19] For convenience, we will use the following nomenclature for the rest of the paper. The proposed method will be called the sequential method.…”

Simulation experiments: Better data, not just big data

“…Adaptive sequential designs are often used, so that each new design point is chosen to reduce the uncertainty associate with model predictions at untested points as much as possible (Kleijnen and van Beers 2004). The community of those designing and analyzing deterministic computer experiments has thus focused on features and a one-at-a-time view of fastness, although some recent work in batch sequential designs (Loeppky et al 2010;Duan et al 2014), may provide additional flexibility for other metamodeling and analysis approaches if the data become too large for kriging software to handle. Brantley et al (2013) describe sequential methods for allocating a fixed computing budget across design points to efficiently identify terms in polynomial metamodels.…”

Sliced Full Factorial-Based Latin Hypercube Designs as a Framework for a Batch Sequential Design Algorithm

“…Recently, Loeppky et al (2010) introduced the notion of batch sequential designs for computer experiments, in particular the bin-based sequential design. The sequential bin structure is established by a set of defining relations.…”

“…In this paper, we present a batch sequential experiment design that uses the idea of sliced space-filling designs from Qian and Wu (2009) and extends the work of Loeppky et al (2010).…”

“…Like Loeppky et al (2010)'s bin-based designs, our design possesses good orthogonality and projectivity at intermediate stages and leads to an OALHD. However, our design does not require preselection of a total number of runs.…”