List of Figures

I.1. Organisation of the Uranie-modules (green boxes) in terms of inter-dependencies. The blue boxes represent the external dependencies (discussed later on).

I.2. Histogram produced using PyROOT

II.1. Diagram of the class TDataServer

II.2. Attributes of TAttribute class

II.3. Graph of the variable sdp

II.4. Scatterplot x2 versus x1 for the geyser data with modification of fields title and unit.

II.5. Example of PDF, CDF and inverse CDF for Uniform distribution.

II.6. Example of PDF, CDF and inverse CDF for LogUniform distributions.

II.7. Example of PDF, CDF and inverse CDF for Triangular distributions.

II.8. Example of PDF, CDF and inverse CDF for Logtriangular distributions.

II.9. Example of PDF, CDF and inverse CDF for Normal distributions.

II.10. Example of PDF, CDF and inverse CDF for a Normal truncated distribution.

II.11. Example of PDF, CDF and inverse CDF for LogNormal distributions.

II.12. Example of PDF, CDF and inverse CDF for a LogNormal truncated distribution.

II.13. Example of PDF, CDF and inverse CDF for Trapezium distributions.

II.14. Example of PDF, CDF and inverse CDF for UniformByParts distributions.

II.15. Example of PDF, CDF and inverse CDF for Exponential distributions.

II.16. Example of PDF, CDF and inverse CDF for a Exponential truncated distribution.

II.17. Example of PDF, CDF and inverse CDF for Cauchy distributions.

II.18. Example of PDF, CDF and inverse CDF for a Cauchy truncated distribution.

II.19. Example of PDF, CDF and inverse CDF for GumbelMax distributions.

II.20. Example of PDF, CDF and inverse CDF for a GumbelMax truncated distribution.

II.21. Example of PDF, CDF and inverse CDF for Weibull distributions.

II.22. Example of PDF, CDF and inverse CDF for a Weibull truncated distribution.

II.23. Example of PDF, CDF and inverse CDF for Beta distributions.

II.24. Example of PDF, CDF and inverse CDF for GenPareto distributions.

II.25. Example of PDF, CDF and inverse CDF for a GenPareto truncated distribution.

II.26. Example of PDF, CDF and inverse CDF for Gamma distributions.

II.27. Example of PDF, CDF and inverse CDF for a Gamma truncated distribution.

II.28. Example of PDF, CDF and inverse CDF for InvGamma distributions.

II.29. Example of PDF, CDF and inverse CDF for a InvGamma truncated distribution.

II.30. Example of PDF, CDF and inverse CDF for Student distribution.

II.31. Example of PDF, CDF and inverse CDF for a Student truncated distribution.

II.32. Example of PDF, CDF and inverse CDF for generalized normal distributions.

II.33. Example of PDF, CDF and inverse CDF for a generalized normal truncated distribution.

II.34. Example of PDF, CDF and inverse CDF for a composed distribution made out of three normal distributions with respective weights.

II.35. Example of PDF, CDF and inverse CDF for a truncated composed distribution made out of three normal distributions with respective weights.

II.36. Import data from an ASCII file

II.37. Content of the ntuple tree contained in "hsimple.root" file.

II.38. Data importation from a TNtuple

II.39. Scatterplot of added attributes

II.40. Graph with a selection definition

II.41. Graph with a definition of Cut

II.42. Different histograms of the same attribute xnorm depending on the method for computing bins. The values are respectively 100(root), 8 from sturges, 7 from fd and scoot.

II.43. Boxplot of attribute x2 of the TDataServer geyser

II.44. CDF graph of attribute x2 of the TDataServer geyser

II.45. Graphs CDF+CCDF of the attribute x2 of the TDataServer geyser

II.46. Scatterplot between attributes x1 and x2 of the TDataServer geyser.

II.47. Scatterplot between attributes x1 and x2 of the TDataServer geyser.

II.48. Graphs of "Tufte" type between the attributes x1 and x2 of the TDataServer geyser.

II.49. Graphs of "Tufte" type between the attributes x1 and x2 of the TDataServer geyser.

II.50. Graphs of "drawPairs" type between the 8 uniformly-distributed inputs and the output of a given problem.

II.51. Graphs of "CobWeb" type between the 8 uniformly-distributed inputs and the output of a given problem.

II.52. Plot resulting from the "drawQQPlot" method, comparing "x2" to a normal distribution.

II.53. Plot resulting from the "drawPPPlot" method, comparing "x2" to a normal distribution.

II.54. Representation of some variables of the Notes sample.

II.55. Representation of the eigenvalues (left) their overall contributions in percent (middle) and the sum of the contributions (right) from the PCA analysis.

II.56. Representation of correlation between the original variables and the PC under study.

II.57. Representation of the data points in the PC-defined plane.

III.1. Schematic view of the input/output relation through a code

III.2. Comparison of the two sampling methods SRS (left) and LHS (right) with samples of size 8.

III.3. Comparison of deterministic design-of-experiments obtained using either SRS (left) or LHS (right) algorithm, when having two independent random variables (uniform and normal one)

III.4. Tufte plot of the design-of-experiments created using a normal and uniform distribution, with a LHS method with three correlation coefficient: 0, 0.45 and 0.9

III.5. Tufte plot of the rank of the design-of-experiments created using a normal and uniform distribution, with a LHS method with three correlation coefficient: 0, 0.45 and 0.9

III.6. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using AMH copula and varying the parameter value.

III.7. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Clayton copula and varying the parameter value.

III.8. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Frank copula and varying the parameter value.

III.9. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Plackett copula and varying the parameter value.

III.10. Comparison of both quasi Monte-Carlo sequences with both LHS and SRS sampling when dealing with two uniform attributes.

III.11. Comparison of design-of-experiments made with Petras algorithm, using different level values, when dealing with two uniform attributes.

III.12. Gaussian Random Field

III.13. Gaussian variograms. Several configurations (in terms of scale factor and variance parameters) are shown as well.

III.14. Sine cardinal variograms. Several configurations (in terms of scale factor and variance parameters) are shown as well.

III.15. Random values for OAT design

III.16. Example of a dataset reduction (the geyser one) using the NeuralGas algorithm, to go from 272 points (left) to 50 one (right)

IV.1. Sketch of the flowrate problem and its variables[BoreHole].

IV.2. Inheritance diagram for the class TLauncher

IV.3. Schematic description of the launcher procedure when using an external code. Yellow boxes show instances of class, and green ones are precision about attributes. The design-of-experiments part can be replaced by an already-existing database.

IV.4. Multi-core computer

V.1. Simplified decomposition of the model creation process into a four important-step recipe.

V.2. Schematic view of the Nisp methodology

V.3. Schematic description of the working flow of an artificial neural network as used in Uranie

V.4. Schematic description of the kriging procedure as done within Uranie

V.5. Estimation using a simple Kriging model

V.6. Residual distribution using a validation database with and without prediction covariance correction.

VI.1. SRC coefficients estimated for the flowrate function.

VI.2. SRRC coefficients estimated for the flowrate function.

VI.3. Histogram of SRC coefficients

VI.4. Morris screening indices

VI.5. Histogram of Sobol's indices

VI.6. Pie chart of Sobol's indices

VI.7. Frequency spectrum from the FAST estimation

VI.8. Histogram of FAST's indices

VI.9. Pie chart of FAST's indices

VI.10. Frequency spectrum from the RBD estimation

VI.11. Histogram of RBD's indices

VI.12. Pie chart of RBD's indices

VI.13. Histogram of JohnsonRW's indices

VI.14. Pie chart of JohnsonRW's indices

VII.1. 3D representation of the Rosenbrock function

VIII.1. Schematic description of the needed steps to define a relauncher procedure

VIII.2. Hierarchy of classes and structures for the evaluation part of the Relauncher module.

VIII.3. Hierarchy of classes and structures for the runner part of the Relauncher module.

IX.1. Hollow Bar

IX.2. Schematic description of the requested steps of an optimisation procedure once this one is performed with Vizir

XI.1. Hierarchy of classes and structures out of Doxygen for the Calibration module

XI.2. Trace distributions split between below and above 100 threshold

XII.1. Results of the macro defined previously to produce variety of test of already implemented distributions

XIV.1. Graph of the macro "dataserverLoadASCIIFilePasture.C"

XIV.2. Graph of the macro "dataserverLoadASCIIFile.C"

XIV.3. Graph of the macro "dataserverLoadASCIIFileYoungsModulus.C"

XIV.4. Graph of the macro "dataserverLoadASCIIFileIonosphere.C"

XIV.5. Graph of the macro "dataserverComputeQuantile.C"

XIV.6. Graph of the macro "dataserverDrawQQPlot.C"

XIV.7. Graph of the macro "dataserverDrawPPPlot.C"

XIV.8. Graph of the macro "samplingFlowrate.C"

XIV.9. Graph of the macro "samplingLHS.C"

XIV.10. Graph de la macro "samplingLHSCorrelation.C"

XIV.11. Graph of the macro "samplingQMC.C"

XIV.12. Graph of the macro "samplingSpaceFilling.C"

XIV.13. Graph of the macro "samplingMaxiMinLHSFromLHSGrid.C"

XIV.14. Graph of the macro "samplingConstrLHSLinear.C"

XIV.15. Graph of the macro "samplingConstrLHSEllipses.C"

XIV.16. Graph of the macro "samplerSingularCorrelationCase.C"

XIV.17. Graph of the macro "launchFunctionDataBase.C"

XIV.18. Graph of the macro "launchFunctionSampling.C"

XIV.19. Graph of the macro "launchFunctionSamplingGraphs.C"

XIV.20. Graph of the macro "launchCodeFlowrateKeyDataBase.C"

XIV.21. Graph of the macro "launchCodeFlowrateKeySampling.C"

XIV.22. Graph of the macro "launchCodeFlowrateXMLSampling.C"

XIV.23. Graph of the macro "launchCodeFlowrateKeySamplingKey.C"

XIV.24. Graph of the macro "launchCodeFlowrateKeyRecreateSampling.C"

XIV.25. Graph of the macro "launchCodeFlowrateKeyRecreateSamplingOutputDataServer.C"

XIV.26. Graph of the macro "launchCodeFlowrateRowRecreateSamplingOutputDataServer.C"

XIV.27. Graph of the macro "launchCodeFlowrateFlagSampling.C"

XIV.28. Graph of the macro "launchCodeFlowrateFlagSamplingKey.C"

XIV.29. Graph of the macro "launchCodeFlowrateKeyFlagSampling.C"

XIV.30. Graph of the macro "launchCodeFlowrateKeywithFlagSampling.C"

XIV.31. Graph of the macro "launchCodeFlowrateKeyFailure.C"

XIV.32. Graph of the macro "launchCodeFlowrateFlagFailure.C"

XIV.33. Graph of the macro "launchCodeFlowrateKeyOATMinMax.C"

XIV.34. Graph of the macro "launchCodeFlowrateFlagOATMinMax.C"

XIV.35. Graph of the macro "launchCodeLevelEOutputColumn.C"

XIV.36. Graph of the macro "launchCodeLevelEOutputRow.C"

XIV.37. Graph of the macro "launchCodeLevelEOutputKey.C"

XIV.38. Graph of the macro "launchCodeMultiTypeKey.C"

XIV.39. Graph of the macro "launchCodeMultiTypeKeyCondensate.C"

XIV.40. Graph of the macro "launchCodeMultiTypeDataServer.C"

XIV.41. Graph of the macro "launchCodeMultiTypeColumn.C"

XIV.42. Graph of the macro "launchCodeMultiTypeRow.C"

XIV.43. Graph of the macro "launchCodeMultiTypeXML.C"

XIV.44. Graph of the macro "sensitivityBrutForceMethodFlowrate.C"

XIV.45. Graph of the macro "sensitivityDataBaseFlowrate.C"

XIV.46. Graph of the macro "sensitivityFASTFunctionFlowrate.C"

XIV.47. Graph of the macro "sensitivityRBDFunctionFlowrate.C"

XIV.48. Graph of the macro "sensitivityMorrisFunctionFlowrate.C"

XIV.49. Graph of the macro "sensitivityMorrisFunctionFlowrateRunner.C"

XIV.50. Graph of the macro "sensitivityRegressionFunctionFlowrate.C"

XIV.51. Graph of the macro "sensitivitySobolFunctionFlowrate.C"

XIV.52. Graph of the macro "sensitivitySobolFunctionFlowrateRunner.C"

XIV.53. Graph of the macro "sensitivityRegressionLeveLE.C"

XIV.54. Graph of the macro "sensitivitySobolLeveLE.C"

XIV.55. Graph of the macro "sensitivitySobolRe-estimation.C"

XIV.56. Graph of the macro "sensitivitySobolWithData.C"

XIV.57. Graph of the macro "sensitivitySobolLoadFile.C"

XIV.58. Graph of the macro "sensitivityJohnsonRWFunctionFlowrate.C"

XIV.59. Graph of the macro "sensitivityJohnsonRWCorrelatedFunctionFlowrate.C"

XIV.60. Graph of the macro "sensitivityJohnsonRWJustCorrelationFakeFlowrate.C"

XIV.61. Graph of the macro "sensitivityHSICFunctionFlowrate.C"

XIV.62. Graph of the macro "sensitivitySobolRankFunctionFlowrate.C"

XIV.63. Graph of the macro "modelerCornellLinearRegression.C"

XIV.64. Graph of the macro "modelerFlowrateLinearRegression.C"

XIV.65. Graph of the macro "modelerFlowrateMultiLinearRegression.C"

XIV.66. Graph of the macro "modelerFlowrateNeuralNetworks.C"

XIV.67. Graph of the macro "modelerFlowrateNeuralNetworksLoadingPMML.C"

XIV.68. Graph of the macro "modelerClassificationNeuralNetworks.C"

XIV.69. Graph of the macro "modelerbuildSimpleGPEstim.C"

XIV.70. Graph of the macro "modelerbuildSimpleGPEstimWithCov.C"

XIV.71. Graph of the macro "modelerTestKriging.C"

XIV.72. Graph of the macro "optimizeFunctionRosenbrock.C"

XIV.73. Graph of the macro "optimizeFunctionRosenbrockNewInputOutput.C"

XIV.74. Graph of the macro "optimizeCodeRosenbrockKey.C"

XIV.75. Graph of the macro "optimizeCodeRosenbrockKeyNewInputOutput.C"

XIV.76. Graph of the macro "optimizeCodeRosenbrockRow.C"

XIV.77. Graph of the macro "optimizeCodeRosenbrockKeyRowRecreate.C"

XIV.78. Graph of the macro "optimizeCodeRosenbrockRowRecreate.C"

XIV.79. Graph of the macro "optimizeCodeRosenbrockRowRecreateOutputDataServer.C"

XIV.80. Evolution of searched parameters a and b throw iterations

XIV.81. Evolution of searched parameters a and b throw iterations

XIV.82. Representation of the output as a function of the first input with a colZ option

XIV.83. Representation of the output as a function of the first input with a colZ option

XIV.84. Representation of the output as a function of the first input with a colZ option

XIV.85. Representation of the output as a function of the first input with a colZ option

XIV.86. Representation of the output as a function of the first input with a colZ option

XIV.87. Representation of the output as a function of the first input with a colZ option when using either the classical or dedicated constructor

XIV.88. Representation of the output data point when the code is asked to fail on purpose.

XIV.89. Graph of the macro "relauncherCodeMultiTypeKey.C"

XIV.90. Graph of the macro "relauncherCodeMultiTypeKeyEmptyVectors.C"

XIV.91. Graph of the macro "relauncherCodeMultiTypeKeyEmptyVectorsAsFailure.C"

XIV.92. Graph of the macro "reoptimizeHollowBarCodeVizir.C"

XIV.93. Graph of the macro "reoptimizeHollowBarVizirMoead.C"

XIV.94. Graph of the macro "reoptimizeHollowBarVizirSplitRuns.C"

XIV.95. The core and its assemblies

XIV.96. Graph of the macro "calibrationMinimisationFlowrate1D.C"

XIV.97. Residual graph of the macro "calibrationLinBayesFlowrate1D.C"

XIV.98. Parameter graph of the macro "calibrationLinBayesFlowrate1D.C"

XIV.99. Residual graph of the macro "calibrationRejectionABCFlowrate1D.C"

XIV.100. Parameter graph of the macro "calibrationRejectionABCFlowrate1D.C"

XIV.101. Trace graph of the macro "calibrationMetropHastingFlowrate1D.C"

XIV.102. Residual graph of the macro "calibrationMetropHastingFlowrate1D.C"

XIV.103. Parameter graph of the macro "calibrationMetropHastingFlowrate1D.C"

XIV.104. Trace graph of the macro "calibrationMetropHastingLinReg.C"

XIV.105. Acceptation rate graph of the macro "calibrationMetropHastingLinReg.C"

XIV.106. Residual graph of the macro "calibrationMetropHastingLinReg.C"

XIV.107. Parameter graph of the macro "calibrationMetropHastingLinReg.C"

XIV.108. Residual graph of the macro "calibrationMinimisationFlowrate2DVizir.C"

XIV.109. Parameter graph of the macro "calibrationMinimisationFlowrate2DVizir.C"

XIV.110. Graph of the macro macro "uncertModelerTestsYoungsModulus.C"