physical uncertainty bounds - c&s tools

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

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LA-UR-14-23193 V&V2014-7090 Slide 1

Physical Uncertainty Bounds “White Box” Uncertainty Quantification

Diane Vaughan, Dean Preston, Mark Anderson ASME V&V Symposium

9 May 2014


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LA-UR-14-23193 V&V2014-7090 Slide 2

Uncertainty quantification must be based on an understanding of how models are constructed

§  Most models of physical categories are complex

§  Conventional uncertainty quantification approaches lead to “lower bounds” at best

§  Physical considerations can produce meaningful bounds


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LA-UR-14-23193 V&V2014-7090 Slide 3

Most models of physics categories are complex hybrids

The caption goes here

Donor Plate

Acceptor Plate

HE Charge


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LA-UR-14-23193 V&V2014-7090 Slide 4

A constitutive model for metal strength is a prototypical example §  Flow stress

§  Burakovsky-Greeff-Preston cold shear modulus model

§  Preston-Wallace model to include temperature dependence

§  Preston-Tonks-Wallace material strength model

G ρ, T( ) =G0 ρ( ) 1−αT̂( ), T̂ = T Tm ρ( )

ϕ = 2Gτ̂

G0 ρ( ) =G0 ρ0( ) ρρ0

!

"#

$

%&

4 3

exp 6γ11ρ01 3 −

1ρ1 3

!

"#

$

%&+2γ2q

1ρ0q −

1ρ q

!

"#

$

%&

()*

+,-

τ̂ = τ̂ s +1ps0 − τ̂ y( ) ln 1− 1− exp −p

τ̂ s − τ̂ ys0 − τ̂ y

"

#$$

%

&''

(

)**

+

,--exp − pθε s0 − τ̂ y( ) exp −p

τ̂ s − τ̂ ys0 − τ̂ y

"

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&''−1

(

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,--

./0

10

230

40

(

)

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+

,

--

τ̂ s =max s0 − s0 − s∞( )erf κT̂ ln γ ξ ε( )()

+,, s0 ε γ

ξ( )β{ }

τ̂ y =max{y0 − y0 − y∞( )erf κT̂ ln γ ξ ε( )()

+,, min y1 ε γ ξ( )

y2 , s0 ε γ ξ( )β(

)*+,-

The melt temperature also requires a model


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LA-UR-14-23193 V&V2014-7090 Slide 5

Uncertainty quantification based on parametric and model selection methods is subject to the curse of dimensionality §  The “curse of dimensionality” has been understood for a long time

§  A number of parameter screening techniques have been developed to reduce dimensionality –  Scientific judgement –  Sensitivity analysis

§  Are we kidding ourselves?

§  Flyer plate example (including model choice) –  74-dimensional parameter space for a fixed choice of models (assuming metal

EOS and melt are known) •  HE burn model: DSD è17 parameters, HE EOS model: JWL è3 parameters

•  Metal strength (2): PTW+BGP+PWè2(11+3+1)=30, Metal damage (2): TEPLA+JC è2(7+5)=24

–  Just looking at some of the discrete model choices discussed in the paper results in more than 300 possible combinations of models

–  Thus, there are ~104 parameters –  Even if only 10 samples per dimension are used, this requires ~105 simulations


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LA-UR-14-23193 V&V2014-7090 Slide 6

Parametric uncertainty methodologies alone cannot explain physical uncertainties

§  Requirements for parametric uncertainties to explain simulation uncertainties are stringent –  Sufficient conditions

•  Models must be correct •  Sampling must preserve both deterministic and statistical constraints

–  Challenge: are there less stringent sufficient conditions? §  There are (at least) four reasons why parametric methods can fail

–  Some models have no parameters –  Model approximations and assumptions

•  Functional forms that approximate physics •  Elimination of dependence of some response quantities on others

–  There are no parameters for regimes with no data –  Parameters are designed to capture mean behavior


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LA-UR-14-23193 V&V2014-7090 Slide 7

Example: approximate functional forms can obviate parametric UQ

G ρ, T( ) =G0 ρ( ) 1−α TTm ρ( )

"

#$$

%

&''

Preston-Wallace model for shear modulus temperature dependence


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LA-UR-14-23193 V&V2014-7090 Slide 8

Example: parametric methods fail in regimes with no parameters and no data

§  Many models span regimes where there is no data

§  Some extrapolate beyond the data –  “Let it ride” model extension –  Guess work (linear, constant slope) –  Theory –  “Virtual” data

§  Some interpolate between data regimes –  Extension mechanisms similar to

extrapolation –  Matching conditions

Preston-Tonks-Wallace saturation stress in the intermediate strain rate regime is an interpolation between regions of low and high strain rates


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LA-UR-14-23193 V&V2014-7090 Slide 9

Including discrete model uncertainty as part of the quantification process doesn’t guarantee success either

§  Parametric uncertainties are typically much smaller than the differences between different models

§  Unexplored uncertainties between models

Discrete model and parametric uncertainty for the binary, linear, and Cochran-Banner flow stress degradation models

Discrete model and parametric uncertainty for the Johnson-Cook, Steinberg-Cochran-Guinan, and Preston-Tonks-Wallace flow stress models


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LA-UR-14-23193 V&V2014-7090 Slide 10

Physical considerations can produce meaningful bounds §  Most models of physical processes are

constructed with a number of internal constraints –  Physical law constraints –  Functional form constraints, e.g., convex

and monotone –  Parameter estimation is often sequential

with a fixed order –  Unless these constraints are explicit in

the fitting process, batch parameter estimation methods will not work in general

§  Meaningful bounds must be based on physics –  Theoretical considerations –  More fundamental simulations such as

molecular dynamics, kinetic theory, or electronic structure codes

Hashin-Shtrikman bounds on Preston-Wallace model for shear modulus temperature dependence

Quantum molecular dynamics upper bounds on metal melt temperature


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LA-UR-14-23193 V&V2014-7090 Slide 11

Summary

§  Most models of physical categories are complex –  Most models are composites of multiple sub-models –  Prototypical example: metal strength

§  Conventional uncertainty quantification approaches lead to “lower bounds” at best –  Parametric uncertainty –  Combined parametric and discrete model uncertainty

§  Physical considerations can produce meaningful bounds –  Model-dependent –  Must be propagated to bounds on quantity of interest


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LA-UR-14-23193 V&V2014-7090 Slide 12

Please read the paper when it appears §  Currently in draft form at Los Alamos (LA-UR-14-20441)

§  Covers five physics categories –  Plasma fusion

•  Li-Petrasso stopping power model –  Material damage

•  Hancock-MacKenzie and Johnson-Cook strain-to-fracture models •  TEPLA porosity growth model •  Binary, linear, and Cochran-Banner flow stress degradation models

–  Prompt fission neutron spectrum •  Maxwellian, Watt, and Madland-Nix spectral models

–  Material strength •  Johnson-Cook, Steinberg-Cochran-Guinan, and Preston-Tonks-Wallace

strength models –  High explosives

•  Lund and Detonation Shock Dynamics programmed burn propagation models •  Jones-Wilkins-Lee products equation of state model


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LA-UR-14-23193 V&V2014-7090 Slide 13

Abstract

This presentation introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switching out available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.

physical uncertainty bounds - c&s tools

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