Getting started with GEM-SA

1. Getting started with GEM-SA

2. This talk • Starting GEM-SA program • Creating input and output files • Explanation of the menus, toolbars, etc. • Description of the project window GEM-SA course - session 3

3. Starting GEM-SA • Double-click the GEM-SA icon to start • The main window appears, with • Menu • Toolbar • Main results area with three tabs • Sensitivity Analysis, Main Effects and Results Summary • Initially all empty • Log window GEM-SA course - session 3

4. The main GEM-SA window menu toolbar Sensitivity analysis output grid Log window GEM-SA course - session 3

5. New project Open project Save project Print output report Edit project Generate input design points Rescale an input Standardise design Copy input design to clipboard Convert input to integer Run the analysis Help Toolbar icons GEM-SA course - session 3

6. Output tabs • When an emulator has been fitted, the contents of these tabs will provide the main results • Sensitivity Analysis. This will report the SA variance decompositions • One line for each input parameter • One line for each pair of inputs, if joint effects are selected • Main effects. This will plot the main effects of the various inputs • Results Summary. This will present numerical summaries of emulator fit and uncertainty analysis GEM-SA course - session 3

7. Log Window output • Tells us • Which training data are being loaded/saved • Transformations applied to the data • Fitted Gaussian process parameters • Summary of cross-validation analysis • Summary of the uncertainty analysis GEM-SA course - session 3

8. Creating a GEM project • To build the emulator we first need 3 files: • Data file of code inputs • Data file of code outputs • GEM-SA project file GEM-SA course - session 3

9. Restrictions on input/output data • Single output • Multiple outputs must be treated individually • GEM can read multiple outputs file, but a single column is specified within a project • Max 30 input parameters • Max 400 training points • The data files are plain text files • One row for each point • Rows can be space or tab delimited GEM-SA course - session 3

10. Generating a new input design • Designs can be generated using the toolbar icon or the menu: Input  Generate… • The design dialog appears GEM-SA course - session 3

11. Generating a new input design • Click OK and fill in the required range for each input • Click OK again GEM-SA course - session 3

12. Editing input designs • If you select a column, you can rescale values of that input or round values to be integers • Designs can be loaded into or saved from this window using the Inputs menu. Use to copy the points to the clipboard for use in other programs GEM-SA course - session 3

13. Types of design • GEM-SA can generate 2 types of design • LP- • Maximin Latin Hypercube designs • Both have good space-filling properties • Ensure all regions of the input space are well represented GEM-SA course - session 3

14. LP- design • Very quick to generate • Deterministic set of uniform points • Increasing the sample size just adds points to the smaller design • Making it useful for sequential analysis • Only have to generate the extra runs GEM-SA course - session 3

15. Maximin Latin hypercube design • Maximin Latin Hypercube designs • Maximise the minimum distance amongst all pairs of points • Can take a long time to generate • Projections also generally space-filling • Lower dimensional projections are also latin hypercubes • Good when only a few inputs are active GEM-SA course - session 3

16. Creating output points • Each row from the input design must be used to generate outputs by running the computer code • One run for each row • Various methods to automate this: • Spreadsheet • Simple, but requires functional form • Script • Only need executable code • Loop through inputs, modify code input file • Modify code to loop through the points • Messy, need source code GEM-SA course - session 3

17. Example: using a spreadsheet • Copy the input design to the clipboard using • Open Excel and paste inputs • Create formula in final column • Copy formula for all rows of the design • Cut and paste special (values) in a new sheet • Save as text file GEM-SA course - session 3

18. Example: using a script • Read simulator’s base input file • Read training inputs file • Loop through training file lines • Replace target inputs using training line • Write new base input file • Run code • Calculate output(s) and add to training output file GEM-SA course - session 3

19. my $pftchangeline = 21; # change line 21 within the input file for each run my @pftchangecols = (11,14,23,19); # columns within pftchangeline to modify my @pftinlh = (0,1,2,3); # ordering of these parameters within training inputs open(BASEINFILE, "input.dat"); # getinitial (fixed) input file used by sdgvmd my @lines = <BASEINFILE>; # and store the input lines in @lines close BASEINFILE; open(LHFILE, "training_inputs.txt"); my $newpftline = $lines[$pftchangeline]; my @newpftpoints = split(" ", $newpftline); while (<LHFILE>){ # assigns each line in turn to $_ chomp; split; my @lhpoints = @_; open(INFILE, "> inputfile.dat"); @newpftpoints[@pftchangecols] = @lhpoints[@pftinlh] # modify lines $lines[$pftchangeline] = join(' ', @newpftpoints)."\n"; print INFILE @lines; close INFILE; `sdgvm0 input.dat`; # run sdgvm0 with modified input # now do something with the output files.... ... } GEM-SA course - session 3

20. The project window • Appears whenever you • Load a project • Edit a project • Create a new project • This window also has 3 tabs • Files • Options • Simulations GEM-SA course - session 3

21. Names for the input files Names for the output files GEM-SA course - session 3

22. How many inputs? What are the input names? Which column from output file? GEM-SA course - session 3

23. What should be calculated, and how? Which joint effects should be calculated? GEM-SA course - session 3

24. What prior mean for the output? How are the inputs uncertain? GEM-SA course - session 3

25. What kind of prediction? What kind of cross validation? GEM-SA course - session 3

26. MCMC control parameters How many realisations of predictions, main and joint effects to generate How many points used to calculate main effects, joint effects GEM-SA course - session 3

27. The options tab

28. Input parameter names • This window appears if you press the Names… button • Giving names is optional, but useful later when looking at GEM-SA output • Ordering can be changed using the arrows GEM-SA course - session 3

29. Selecting joint effects • Select calculate joint effects if in sensitivity analysis you want to see the joint effects (interactions) of pairs of inputs as well as their individual effects • Use Inputs to include in joint effects panel to select which ones • Default All inputs computes joint effects for all pairs • Can take a lot of computation • To compute only the joint effects between selected inputs, deselect All inputs and select the two or more inputs whose joint effects are of interest GEM-SA course - session 3

30. Other checkboxes • Sum effects • There are two ways to plot the joint effect of two inputs: • A combined effect in which the value plotted is the mean output value at that combination of input values • A pure interaction, in which with the main effects of those inputs are subtracted from the combined effect • Select sum effects if you want to see combined effects, and deselect it to see interactions • This selection is ignored if you don’t ask for joint effects to be computed GEM-SA course - session 3

31. Other checkboxes • Code has numerical error • We generally assume that the model output is computed exactly every time • So the meta-model passes exactly through all the training points • There are two situations in which this assumption is not right • Your code has numerical errors which you want to smooth out • Your code is stochastic and the output values have random noise • Selecting code has numerical error turns the assumption off • The variance of the error will be estimated as part of the fitting process • The meta-model will smooth out the training points to a degree depending on the estimated error variance • Can make the fitting process quite unstable, so beware! GEM-SA course - session 3

32. Other checkboxes • Use MCMC for emulator parameters • By default, GEM-SA estimates the underlying smoothness parameters and then pretends that the estimates are exact • Selecting use MCMC for emulator parameters takes into account uncertainty in the fitting of the emulator • Slows down the computation substantially, often with minimal effect on the results • Auto-tune Metropolis algorithm • Use only with MCMC • If not selected, you must supply a tuning file GEM-SA course - session 3

33. Input uncertainty options • These options are for specifying what kind of distribution each uncertain input has • There are a limited range of options • All unknown, product normal/uniform • Inputs are independent, with either normal or uniform distributions • All known • No uncertainty analysis required • Some known, rest product normal/uniform • Some input values will be fixed (in the dialog window or in a prediction file) • Others will be given independent distributions, either normal or uniform GEM-SA course - session 3

34. Input uniform ranges • If you say that some or all have uniform distributions, a window appears (when you click OK) to specify ranges • Option to use ranges in input data file Some fixed, rest uniform All uniform GEM-SA course - session 3

35. Input normal parameters • If you say that some or all have normal distributions, a window appears (when you click OK) to specify the mean and variance of each distribution • Option to use ranges in input data file Some fixed, rest normal All normal GEM-SA course - session 3

36. Prior mean options • The emulator will fit better if it knows roughly how the output is expected to respond to the inputs • You have just two choices • If you expect to see a trend in the output in response to changes in its inputs, select linear term for each input • Otherwise, selecting constant mean results in no overall trends being expected or fitted GEM-SA course - session 3

37. Selecting prediction type • Having fitted the Gaussian process emulator, GEM-SA can predict what the output would be if the computer code were run at new input sets • These are specified in a prediction file • If there is no prediction file, selecting the prediction type has no effect • Predictions can be • Simulated realisations of outputs at the prediction inputs • Similar to main effect outputs • Takes account of correlation between predictions • Marginal means and variances of outputs at the prediction inputs • Faster to compute, especially with many prediction points • Easy to interpret GEM-SA course - session 3

38. Selecting cross validation type • Cross-validation is a way of checking the validity of the predictions made by GEM-SA • The idea is to fit the emulator leaving out some of the training data points, then predict the missing points and see how well the predictions do • Choice of none, leave-one-out or leave final 20% out • Leave-one-out • Hyper-parameters use all data and are then fixed when prediction is carried out for each omitted point • Leave final 20% out • Hyper-parameters are estimated using the reduced (80%) data subset GEM-SA course - session 3

39. The files and simulations tabs

40. GEM-SA files • You always have to specify an Inputs File and an Outputs File • You only need to specify a Prediction Inputs File if you want to generate predictions • You only need to specify a Metropolis-Hastings Tuning File if you select MCMC for computation and deselect auto-tuning • The Main effects file will always be created when you do sensitivity analysis • The Joint Effects file will be created if you ask for joint effects to be computed • The Predictions File will be created if you ask for predictions (by specifying a Prediction Inputs File) • It will contain simulated predictions or prediction means • The Predictions Variance File is created if you ask for predictions and specify prediction means and variances GEM-SA course - session 3

41. Simulations • The first three of these settings apply only if you select MCMC computation • For expert users only! • You could choose the number of simulations that are computed for each main effect and interaction • But the default is generally plenty • You might want to increase the number of points on each main effect • To get more detail in the plots • But at the cost of longer computations GEM-SA course - session 3