Assessment of Predictive Capability

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Assessment of Predictive Capability. James Paul Holloway. CRASH Review Meeting October 19 2009. Several initial UQ projects are complete. Investigated (with CRASH 1D) the importance of: Initial radiation field, boundary conditions, EOS, initial field fit - PowerPoint PPT Presentation

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  • Assessment of Predictive CapabilityJames Paul HollowayCRASH Review MeetingOctober 19 2009

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    Several initial UQ projects are completeInvestigated (with CRASH 1D) the importance of:Initial radiation field, boundary conditions, EOS, initial field fitExplored (with Hyades 1D) sensitivity of shock location at 13 ns over 15-D input spaceIncluded experimental, physical and numerical parametersConstructed a physics informed emulator (PIE) for CRASH 1D initial fields at 1.3 nsIdentified 40 scalar parameters to describe Hyades output fieldsConstructed an emulator for these over the input variablesInvestigated of sensitivity of PIE data to 15 Hyades inputsConstructed a predictive model over 8-D input space CRASH 1DPerformed sensitivity study of 3D CRASH over a 4-D input spaceSee later talks by Fryxell & Binghamand various posters

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    Predictive RoadmapAnalysis elements:Experimental designSensitivity studiesYear 1 & 2Integration of team membersExercise of analysis tools using Hyades, CRASH 1D and CRASH multi-DYear 3Use analysis & experiments to identify and improve modeling elements quantify sources of errorNumerical error estimationUncertainty due to experimental and physics parametersSuggest experiments based on UQ analysisImprove preprocessor (PIE) and extend to 2DDemonstrate improved predictionsYear 4Analysis of 5th year experimental regime to estimate sensitivities and predictive distributionSuggest experiments based on UQ analysisYear 5Provide improved predictions of 5th year experiment and prediction pdfEmulator constructionCalibration of physics parametersEstimating predictive distributions

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    We are heading towards the year 5 elliptical tubeDo computations and experiments with circular tubesCan do computations with elliptical tubesMust predict output y and its pdf for the elliptical tubeYear 1-4experimentsYear 5 experimentInput space xSimulations

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    We will use statistical modeling to guide improvement of the CRASH codeUse assessment of predictive capability to guideImprovement in CRASH code physics and numericsIdentification of needed field experiments or diagnosticsto produce predictions for an extrapolated field experimentAim towards predicting results in an unexplored region of the field experimental input space (the oval tube)Carry this out with a first principles physics code, avoiding the use of tuning parameters or unphysical choices of physics parametersCodeAssessmentExperiments

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    Predictive science is more than predictionKnowledge of the sensitivity of the output to variations in the inputWhich input parameters, when varied over their probable ranges, generate the significant variations in outputAn understanding of the significant sources of uncertainty in outputAn estimate of the predictive distribution of outputs overUncertainty in physics parametersUncertainty in experimental parametersUncertainty in statistical fitting parametersSuccessful prediction means that the experimental result is, with reasonable probability, within the range predicted by the code

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    CRASH maps inputs to output

    We want to characterize the variations in around interesting ranges of inputs SensitivitiesPredictive distributionsNumerics converged sufficiently to be small contributor to overall uncertaintyWe understand CRASH as a map from input to outputFocus ofcurrentUQ efforts

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    Some of our key inputs include:Laser energy and pulse shapeInitial Xe pressureBe drive disk thicknessTime of radiograph observationTube geometry

    These are uncertainThese are uncertainThese introduce errorEOS dataOpacities Mesh parametersLimiter choiceTime step controller

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    Key outputs include:Shock position at observation time Distance of edge of shock from tube wallAngle of xenon edge just downstream of shockAverage thickness of Xe layer X-ray radiograph from experiment with average velocity 140 km/sec at 14 ns

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    We have explored the influence of problem setup Initial radiation fieldLeft (irradiated) boundary locationEOS treatmentInitial field fitVaried mesh, initial field, boundary location

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    Use a set of 10 key spatial locations and interpolate hydrodynamic fields at 1.3 nsCreate mapping of Hyades inputs to these 40 parameters Uncertainty in fit will contribute uncertainty to CRASH resultsWe have build a physics informed emulator: PIE

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    Sensitivity analysis using statistical fittingSample input space (Latin hypercube sampling)Compute outputsFit a modelGaussian Process model Flexible regression modelsEstimate global sensitivity due to an input by:perturbing input variable randomly over samplesrefittingcomputing RMS differenceEstimate local sensitivities using length parameters from GP modelMarginalize over other variables to explore variation due to one or two variablesThe LHD used for CRASH 3D sensitivity study

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    We can identify important influences on shock locationBased on 512 Hyades runs and MART fitBe ThicknessLaser EnergyXe DensityBe and Xe gammasBe and Xe opacity scale factorsInforms selection of parameters for 3D studySee related study on CRASH 3D in Fryxells talk

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    Construct predictive model of output along with posterior calibration pdf Combine with estimated or input ranges to account for input uncertaintySuch a model provides:Mean and variance of output predictive distributionTool to explore error in the model relative to experimentApproach to determine a next experiment or simulation to reduce uncertaintyA predictive model provides a pdf of outputs

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    CRASH 1D Predictive Model Construction

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    MeasurementsSelect 8 as training data, predict a 9th.

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    The predictive model gives us a way to explore physicsData for model are field experiments and set of code runsModel data as sum of 3 terms:Emulator of the code (Gaussian process model)Model discrepancy (Gaussian process model)Measurement error

    Large discrepancy compared to measurement uncertainty implies prospects for prediction are poorphysics or numerics of code is wrongor measurements are misleadingCode improvements can be judged against reduction in discrepancy in key regions of input spaceMust avoid conflating discrepancy with calibration

    Results using CRASH 1D in Binghams talk

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    Our immediate next steps build on this workExplore the CRASH 1D Predictive ModelExplore discrepancy over inputs and reflect on the physicsCompare joint computation of discrepancy and calibration with sequential calibration and computation of discrepancyRepeat with multi-group diffusion and explore discrepancyInclude uncertainty in initializationQuantify sources of uncertaintyUse predictive model to suggest new code runs and experimentsMinimize uncertaintyMinimize discrepancyMove towards a predictive model using CRASH multi-DPropagate uncertainty information through EOS/Opacity model

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    We are heading towards the year 5 elliptical tubeWe can performExperimental designSensitivity studiesEmulator constructionCalibration of physics parametersEstimating predictive distributionsNext stepsUse analysis & key experiments to identify and improve key modeling elements quantify sources of errorNumerical error estimationUncertainty due to experimental and physics parametersSuggest experiments based on UQ analysisImprove preprocessor (PIE) and extend to 2DDemonstrate improved predictionsAnalysis of 5th year experimental regime to estimate sensitivities and predictive distributionSuggest experiments based on UQ analysisProvide improved predictions of 5th year experiment and prediction pdf

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    Related PostersAutomatic Detection of Shock Wave FeaturesN Patterson, R. P. Drake, K ThorntonBuilding a Dataset of Results Modeling Radiative Shocks in 1D HYADES for Uncertainty QuantificationM. J. Grosskopf, R. P. Drake, B. Fryxell, F. W. Doss, C. C. Chou, D BinghamCalibrating HYADES as initial conditions for CRASHMJ Grosskopf, R. P. Drake, B Torralva, F. W. DossGaussian Process Regression and Bayesian MARS for CRASH Initialization with HAYDESDuchwan Ryu, Ryan McClarren, Anirban Mondal, Zach Zhang, Ashin Mukherjee, Jason Chou, Bani Mallick, Derek Bingham, Bruce Fryxell, Vijay Nair, Ji ZhuGradient-Enhanced Stochastic Expansion: A Survey of Response Surface Construction MethodsColin Miranda, Krzysztof Fidkowski, Kenneth PowellPreliminary 1D CRASH Resolution Study / Variable ScreeningChuan-Chih (Jason) Chou, Paul DrakeVerification of Uncertainty Quantification SoftwareBruce Fryxell, Jason Chou, Ashin Mukherjee, Zach Zhang, Vijay Nair, Mike Grosskopf, Derek Bingham, Bani Mallick, Duchwan Ryu

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    Questions?

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    Additional Slides Follow

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    CRASH Personnel directly engaged in UQBruce Fryxell, James Holloway, Paul DrakeDerek Bingham, Vijay Nair, Bani MallickMarvin Adams, Ryan McClarrenJason ChouChris FidkowskiMike GrosskopfAnirban MondalAshin MukherjeeAvinash PrabhakarDuchwan RyuZach ZhangJi Zhu

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    Sensitivity study shows mesh convergenceAverage shock location at 13 ns convergedAverage shock location at 13 ns converged

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    Hyades emulator construction and sensitivity runs15 dimensional input space sampled512 point space filling LHD constructedTAMU constructed PIE emulator for 1.3 nsUM carried out sensitivity analysis for shock location at 13 ns

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    Experimental Design for CRASH 1D analysis256 Points over 8 dimensions (4 thetas, 4 xs) orthogonal array based space-filling LHD8 purely for computer run inputs64 Points over the product space

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