stilt-package {stilt}

Separable Gaussian Process Emulator

Description

'Stilt' is used for interpolating multivariate data in multivariate space. It is tailored to the case of interpolating ("emulating") regularly spaced time-series of computer model output between the model input parameters, but can be also used more broadly (e.g., for output in the form of regularly-spaced spatial 1D transects, or for interpolating time-series between locations on the Earth's surface). The interpolation technique relies on a separable Gaussian Process emulator. Package consists of functions to fit the Gaussian Process emulator, to interpolate to (predict at) a given model input setting, and to validate the emulator using cross-validation. In addition, a function is provided to plot model response surface as generated by the emulator as a function of two model parameters. The package works both on one and multi-parameter ensembles, with an exception of the 'rsurface.plot' function, which by definition is restricted to 2+ parameter ensembles. The emulator is restricted to multivariate model output and is not designed to work on interpolating a single scalar.

Details

Package:	stilt
Type:	Package
Version:	1.3.0
Date:	2017-08-15
License:	GPL-3
LazyLoad:	no

Disclaimer

This package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. In addition, the authors maintain no responsibility for any possible code errors or bugs.

Summary of main functions

emulator

Fits a separable Gaussian Process emulator to ensemble model output

predict.emul

Predicts using a Gaussian Process emulator

rsurface.plot

Plots a 2D model response surface

test.csv

Cross-validates an emulator by removing one or many model runs, training the emulator on the remaining runs, and then predicting at the withheld model runs

test.all

Tests an emulator using leave-one-out cross validation

sep.cov

Constructs time and parameter covariance matrices

Summary of datasets

Data.1D.model and Data.1D.par

Model output and parameter settings for a simple 1-parameter ensemble example

emul.1D

Gaussian Process emulator that has been fit to the aforementioned model ensemble output

Data.AR1.Korea.model and Data.AR1.Korea.par

Temperature variability and future change for 29 CMIP5 global climate models

Data.UVic.model and Data.UVic.par

Model output and parameter settings for temperature anomaly output from 3-parameter ensemble of climate model UVic ESCM

Data.Sicopolis.model and Data.Sicopolis.par

Model output and parameter settings for ice mass loss output from a 5-parameter ensemble of ice sheet model SICOPOLIS

emul.Sicopolis

A Gaussian Process emulator that has been fit to the SICOPOLIS ensemble output

Limitations and Caveats

1. The emulator (like any other available software packages) will not work well for 'jagged' model response surfaces (high nugget): predictive uncertainty will be too high.

2. The emulator is restricted to output at regular intervals in time and space

3. The code has not been tested under conditions of extreme high / extreme low input parameter range, output time(space) coordinates range, and output range (an example would be model output ranging from -1E20 to 1E20, etc.). In such cases it is recommended to re-scale the time(space) coordinates vector, the input parameters, and/or the model output.

4. The emulator will not work on scalar model output – it requires multivariate data

5. The emulator assumes a separable covariance function, and stationarity of the covariance part of the Gaussian process.

6. The optimization of the emulator parameters degrades dramatically (and increases in time) as a function of number of free parameters. Hence, the emulator might be of limited use for large parameter ensembles

7. The emulator authors are not responsible for any code errors and/or bugs

Author(s)

Roman Olson, Won Chang, Klaus Keller and Murali Haran

Maintainer: Kelsey Ruckert <[e-mail]>

References

R. Olson and W. Chang (2013): Mathematical framework for a separable Gaussian Process Emulator. Tech. Rep., available from
www.scrimhub.org/resources/stilt/Olson_and_Chang_2013_Stilt_Emulator_Technical_Report.pdf.

C. E. Rasmussen and C. K. I. Williams (2006): Gaussian Processes for machine learning, the MIT press, available from www.gaussianprocess.org/gpml/