DynamicGP-package {DynamicGP}

Modelling and Analysis of Dynamic Computer Experiments

Description

For emulating dynamic computer experiments, three functions are included. The function svdGP fits full SVD-based GP model which is computationally demanding for large-scale dyanmic computer experiments. As is well known, the time complexity of fitting a GP model is O(N^3) where N is the number of training/design points. Since fitting a common GP model for really large N would be computationally burdensome, we fit local SVD-based GP models on a sequentially selected small neighborhood set for every test inputs. The function knnsvdGP fits K-nearest neighbor SVD-based GP models which selects neighborhood sets based on the Euclidean distance with repect to the test points. The function lasvdGP fits local approximate SVD-based GP model using the new algorithm proposed by Zhang et al. (2018).

The lasvdGP is an extension of the local approximate GP (laGP) model developed by Gramacy and Lee (2015) for the emulation of large-scale scalar valued computer experiments. The neighborhood selection and SVD-based GP model fitting algorithm is suitable for parallelization. We use both the R package "parallel" and the OpenMP library for this task. The parallelization can achieve nearly linear speed since the procedure on each test point is independent and identical.

For the inverse problem in dynamic computer experiments, we also provide three functions. The function ESL2D minimizes the expected squared L_{2} discrepancy between the target response and the simulator outputs to estimate the solution to the inverse problem, where the expectation is taken with respect to the predictive distribution of the svdGP model. A naive estimation approach SL2D simply minimizes the squared L_{2} discrepancy between the target response and the predicted mean response of the SVD-based GP model. The function saEI performs the squential design procedure for the inverse problem. It selects the follow-up design points as per an expected improvement criterion whose values are numerically approximated by the saddlepoint approximation technique. Details of the three methods for the inverse problem are provided in Chapter 4 of Zhang (2018).

Author(s)

Ru Zhang [e-mail],

C. Devon Lin [e-mail],

Pritam Ranjan [e-mail]

References

Gramacy, R. B. and Apley, D. W. (2015) Local Gaussian process approximation for large computer experiments, Journal of Computational and Graphical Statistics 24(2), 561-578.

Zhang, R., Lin, C. D. and Ranjan, P. (2018) Local Gaussian Process Model for Large-scale Dynamic Computer Experiments, Journal of Computational and Graphical Statistics,
DOI: 10.1080/10618600.2018.1473778.

Zhang, R. (2018) Modeling and Analysis of Dynamic Computer Experiments, PhD thesis, Queen's University, ON, Canada.