CRASH UQ Program: Overview & Results James Paul Holloway CRASH Annual Review Fall 2010

We predict what we have not yet measured Do calibration and validation experiments in Years 1-3 Do code runs to characterize and improve predictions around those experiments Do code runs around year 4 & 5 experiments Use physics (code) and our characterization of uncertainties in new region of inputs to predict year 4 & 5 Year 1-3 experiments Years 4 & 5 experiments Simulations

W e have several outputs & inputs Outputs ( ) Shock location (SL) Axial centroid of dense Xe (AC) Area of dense Xe (A) Shock breakout time (BOT) Inputs ( ) Observation time of shock location, axial centroid, area Laser energy Be disk thickness Xe fill gas pressure Calibration parameters (  ) Vary with model Shock location Centroid of dense Xe Area of dense Xe Fixed window

Using a variety of methods we have… explored sensitivity of SL to screen important inputs Influence plots, GPM correlations explored SL output surfaces to understand sensitivity SourceSL Uncert. Be Gamma~ 0.15 mm Initialization~ 0.10 mm Discrepancy~ 0.10 mm Be Disk Thickness~ 0.10 mm Xe Fill Pressure~ 0.04 mm Laser Energy~ 0.01 mm Exp. Uncert.~ 0.10 mm Importance of electron flux limiter led to 2009 calibration experiment definition Sensitivity of triple point location led to new integrated metrics

Integrated metrics: shock location Extract shock location from piecewise constant fits over a fixed region (window) of the radiograph Four segment fit representing unshocked, shocked disk, entrained Xe annulus, trailing plasma Knot locations optimized for minimal MSE First knot is a predicted output (SL)

Integrated metrics: mask to large optical depth Add slide with 104 CRASH runs windowed to 100 micron radius & 2 mm long

Integrated metrics: dense Xe centroid & area Define threshold based on the unshocked Xe optical depth Extract Axial Centroid of Xe above the threshold Insensitive to threshold over wide range Extract Area of Xe above the threshold Varies smoothly with threshold Additionally, and for radial metrics

The 1024 point run set Hyades and CRASH 2.0 in 1D 6D input space (4 x’s and 2 thetas) Orthogonal LHD with space filling criterion Best estimates of x uncertainties at time of problem definition (we know more now) We also have a 104 point run set in 2D

We have experiments for calibration and experiments for characterizing uncertainty 2008 Shock Location measurements at 13, 14 and 16 ns 2009 Shock Breakout Time (BOT) measurements 2010 Shock location at 20 and 26 ns (SL2010) Currently we are predicting SL2010 using: BOT for calibration SL from 2008 to characterize predictive error The process involves using a pair of Kennedy-O’Hagen models and moving data from one to the next

We use a model structure for calibration, validation & uncertainty assessment Measured in calibration experiments with specific x and unknown theta (few of these) Computed with specific values of x and theta (lots of these) Models discrepancy between reality and code – speaks to validation Replication error Fits code over input space Kennedy & O’Hagan 2000, 2001 experimental input physics or calibration input

Leave one out predictions tell us how we are doing 2008 SL experiments 2009 BOT experiments

Calibration using Breakout Time (BOT) Predicting SL at 20 and 26 ns Assessing Shock Location (SL) prediction Prediction and estimate of uncertainty Move discrepancy and replication error to new region of inputs small  model calibrates

Posterior distribution of electron flux limiter is useful for other outputs Consistent with BMARS based calibration of BOT by Stripling (see poster)

Posterior distribution of laser energy scale factor is useful for other outputs

Predictive Study Use calibration experiments (2009) and validation experiments (2008) with CRASH to construct model Use model to predict at 20 and 26 ns Sample 50 sets of x values For each x sample 200 theta values Sample shock location from model Construct predictive intervals for: Code alone (red) Entire model: code, discrepancy, replication error (blue)

Median SL ns ns We have 95% predictive intervals Repeat this predictive study using the 104 runs initialized using Hyades 2D and 2D CRASH

Future studies need to cope with finite computational resources Use simulations of varying fidelity in calibration and prediction Because computational costs are high, we need to be strategic about what runs we do Highly resolved 2D Multigroup and 2D Gray Well resolved 3D Gray Lower resolution 3D Multigroup A first study can be tried with 1D CRASH and 2D CRASH