Quantifying Propagation Uncertainties in Computer Code Chains
Technical Report,01 Jan 2015,01 Jan 2018
XL Scientific Albuquerque United States
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We present a novel approach to quantifying uncertainties in the values of the output variables of computer codes used for numerical simulations of scientific and other processes of interest, where these uncertainties are a result of 1 uncertainties in the true real-world values of the code input variables, 2 uncertainties in the forms and details of the code models, and 3 numerical uncertainties arising from the need to perform arithmetic computations via discretization of the often continuum model equations and from the use of finite precision. We apply our uncertainty quantification UQ methodology to both a single, stand-alone code as well as to an N-member code chain in which the jth code in the chain produces a value of an output variable having uncertainty quantified in our sense and which output variable value subsequently serves as an input variable value for the j1th successor code in the chain, which j1th code then itself produces a value of an output variable also having uncertainty quantified in our sense. The uncertainties in the values of all input and output variables are represented in our formulation by probability density functions PDFs. Our entire formulation is analytic and requires 1 two uncertainty constants for each code in the chain, 2 knowledge of or estimates of upper and lower bounds for the values of all code variables of interest, and 3 the functional relationships between all input and output variables of interest which may be available either analytically or computationally in the absence of uncertainty considerations.