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Assessing the Reliability of Complex Models Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012) / Chapter Skim
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2 Sources of Uncertainty and Error
Pages 19-30

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From page 19...
... To proceed to a more fine-grained understanding and taxonomy of sources of analytic uncertainty and error, it will be helpful to consider a specific situation -- one that is simplified sufficiently to be tractable and yet complex enough to be 1 The terms analyst and decision maker refer to the roles that the two parties fulfill. Someone who is a decision maker in one context may well be an analyst in another.
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From page 20...
... This also depends on the application under consideration. In this rod and plate example, it may be that the primary QOI Density at 0.00e+00 seconds g/cm3 FIGURE 2.1 Aluminum rod impacting a cylindrical aluminum plate.
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From page 21...
... The experimental measurements permit an assessment of the difference between the computational model and reality, at least under the conditions of the available experiments, a topic that is discussed throughout Chapter 5, "Model Validation and Prediction." Note that uncertainties in experimental measurements also impact this validation assessment. An important point to realize, for the purposes of this discussion, is that the computational model results all depend on the many choices made in developing the computational model, each potentially pushing the computed QOI away from its counterpart from the true, physical system.
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From page 22...
... However, the specific form taken by the dissipative component of the stress tensor, tdiss, relies on ap proximations, particularly involving the thermodynamic specification of the system. If, following the analysis mentioned above, it is decided that the rod and plate system will be modeled as a viscous fluid, then the viscous component of the stress tensor can be expressed as a function of the shear and bulk viscosities, hs and hn: 2 · · τ diss = τ NS = 2ηsεkl + (2ηv – η )
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From page 23...
... Finding: Common practice in uncertainty quantification has been to focus on the propagation of input uncertainties through the computational model in order to quantify the resulting uncertainties in output quantities of interest, with substantially less attention given to other sources of uncertainty.
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From page 24...
... Algorithmic inadequacies and resolution inadequacies stem from a common cause: most mathematical models in computational science and engineering are formulated using continuous variables and so have the cardinality of the real numbers; but all computers are finite. In most cases, derivatives are finite differences and integrals are finite sums.
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From page 25...
... , manufactured solutions, 3 and extensive testing are all attempts to ensure that as many of the lines of code as possible are error-free. It may be trite but is certainly true to say that a single bug may be sufficient to ensure that the best computational model in the world, run on the most capable computing platform, produces results that are utterly worthless.
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From page 26...
... A typical strategy to use in constructing effective models is to require that the effective model obey whatever symmetries happen to be present in the full model. In fluid dynamics, for example, one would prefer to have a subgrid model possess the symmetries of the full Navier-Stokes equations.4 Often, however, retaining the full symmetry group is not practicable.
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From page 27...
... If the climate model were simply run at its usual setting for the parameters, one would obtain only one result, corresponding to an increase of 3.4 degrees. Note also that the initial state of the climate is unknown; to reflect this, a total of 2,578 runs of the climate model were made, varying both the model parameters and the initial conditions.
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From page 28...
... That this is the case for climate models is indicated by the difficulty of simultaneously tuning climate models to fit numerous outputs; global climate predictions can often be tuned to match various statistics from
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From page 29...
... 2.10.2 Future Directions for Research and Teaching Involving UQ for Climate Models In spite of the challenges in the formal implementation of UQ in climate modeling, the committee agrees that understanding uncertainties and trying to assess their impact is a crucial undertaking. Some future directions for research and teaching that the committee views as highly promising are the following: 1.
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From page 30...
... 2009. Bayesian Modeling of Uncertainty in Ensembles of Climate Models.
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Key Terms

  • initial conditions
  • climate model
  • computational model
  • model parameters
  • complex models

  • prediction uncertainty
  • global mean
  • mean temperature
  • mathematical model
  • decision maker

  • climate modeling
  • effective model
  • computational expense
  • governing equations
  • uncertainty quantification

  • rod impacting
  • stress tensor
  • computational science
  • analytic uncertainty
  • cylindrical aluminum

  • computed qoi
  • experimental measurements
  • model results
  • model predictions
  • numerical models

  • initial state
  • numerical hydrodynamics
  • effective models
  • resulting prediction
  • final prediction


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