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Uncertainty Quantification

“… as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

Albert Einstein, Geometry and Experience, Lecture before the Prussian Academy of Sciences, January 27, 1921

Illinois Rocstar LLC is an Engineering Simulation Science company. As the US and world gain increasing skills and dependence on high performance computing and simulation, it is increasingly critical that we treat computing as the science it is, and acknowledge the inherent uncertainties in it’s use. Quantification of uncertainties in the results of large, parallel simulations is imperative if those results are to be useful in engineering design or scientific exploration. There are many methods for performing so-called “Uncertainty Quantifications (UQ),” for simulations, but for simulations where the problems are large and long-running, with many uncertainties, the costs can be prohibitive to use most of the known techniques. Trying to propagate hundreds of uncertain parameter distributions through a long-running simulation can require hundreds, thousands, or even millions of code runs depending upon the technique being used. Illinois Rocstar has, under a Phase II SBIR contract from NASA, codified a methodology to get around some of these problems. The Illinois Rocstar Reduced-Order Clustering Uncertainty Quantification (ROCUQ) technique has been coded as a C-program using the Sandia National Laboratories Dakota package for certain facilities. The ROCUQ methodology takes your large, long-running simulation, a user-defined reduced-order model of your problem, and a two-step sampling approach to estimate output uncertainty distributions with effectively any number of input parameter distributions, and only a few long-running simulations. It does not yet treat modeling, or other non-parameter uncertainties, but can be a useful engineering tool for UQ with HPC codes.


Uncertainty Distribution of small rocket head-end-pressure in time, compared to three experimental measurements

The ROCUQ code and report resulting from the Phase II SBIR effort are both freely available. You may download the report here: IllinoisRocstar_ROCUQ_FinalReport. There are a number of examples of application of ROCUQ in the report in several different scientific disciplines. If you are interested in obtaining the software package, please contact sales@illinoisrocstar.com. It will be provided free-of-charge. Assistance or support may be obtained through Illinois Rocstar for a fee. ROCUQ has been compiled against Dakota 5.3.

An early technical article on the development of ROCUQ may be found at:

Brandyberry, M.D. (2008) “Thermal Problem Solution Using a Surrogate Model Clustering Technique,” Computer Methods in Applied Mechanics and Engineering, Vol. 197(29-32), pp. 2390-2407.

Contact Dr. Mark Brandyberry (mdbrandy@illinoisrocstar.com) to obtain a copy of the article if you do not have access elsewhere.

You can download the source archive with examples and documentation from here.