Abstract
We present two recently released R packages, DiceKriging and DiceOptim, for the approximation and the optimization of expensive-to-evaluate deterministic functions. Following a self-contained mini tutorial on Kriging-based approximation and optimization, the functionalities of both packages are detailed and demonstrated in two distinct sections. In particular, the versatility of DiceKriging with respect to trend and noise specifications, covariance parameter estimation, as well as conditional and unconditional simulations are illustrated on the basis of several reproducible numerical experiments. We then put to the fore the implementation of sequential and parallel optimization strategies relying on the expected improvement criterion on the occasion of DiceOptim’s presentation. An appendix is dedicated to complementary mathematical and computational details.
Highlights
Numerical simulation has become a standard tool in natural sciences and engineering
We have presented two packages, DiceKriging and DiceOptim, for Kriging-Based design and analysis of computer experiments
Parameters relying on a global optimizer with gradient like the genoud algorithm of the package rgenoud, and for the efforts done in order to recycle intermediate calculations as often as possible and avoid calculating twice the same quantities
Summary
Numerical simulation has become a standard tool in natural sciences and engineering. Used as cheaper and faster complement to physical experiments, simulations sometimes are a necessary substitute to them, e.g., for investigating the long term behavior of mechanical structures, or the extreme risks associated with geological storage (e.g., CO2 sequestration or nuclear waste deposit). Several R (R Development Core Team 2010) packages like spatial (Venables and Ripley 2002), geoR (Ribeiro and Diggle 2001), gstat (Pebesma 2004), and RandomFields (Schlather 2012) propose a wide choice of functionalities related to classical 2- and 3-dimensional geostatistics These packages are not suitable for applications in higher dimensions, for which similar Kriging equations but specific parameter estimation techniques have to be used. BACCO contains the packages calibrator and approximator, which offer an implementation of the calibration and multi-objective models introduced by Kennedy and O’Hagan (2000, 2001), as well as a first R package implementing universal Kriging (UK) in a Bayesian framework, emulator This package considers one choice of priors that provide analytical results, and is limited to the Gaussian correlation function. In particular we give a table of computational cost and memory size of the main procedures (Appendix C.3), some comments about speed (Appendix C.4), and two tests of trustworthiness for the covariance estimation algorithms (Appendix D)
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