DynamicGP-package | R Documentation |

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).

Ru Zhang heavenmarshal@gmail.com,

C. Devon Lin devon.lin@queensu.ca,

Pritam Ranjan pritamr@iimidr.ac.in

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.

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