Keywords: uncertainty quantification, evidence theory, multimodel approach, simulation.

Due to various sources of uncertainty, the results of a simulation deviate from the exact solution. In [1,2], we suggested a methodology based on the Dempster-Shafer theory of evidence [3] for quantifying the total uncertainty in the results of simulation. The total uncertainty is the combined contribution from all uncertainty sources. The methodology requires experimental (or observational) data to compare the results of the simulations with. Having a measure for quantifying the total uncertainty in the results of the simulation, one can compare the performance of different models.

However, one cannot predict which model will perform better, if no experimental data is available to compare with. Even if experimental data is available, judgment in a favor of one of the models may also be hard to make. A promising alternative to simulations conducted with a single model is the multimodel approach, where the results of several simulations conducted with different models are combined into a single solution. The multimodel approach proved to be very useful in practical applications, particularly, in meteorology, artificial intelligence, and risk assessment.

We developed the multimodel approach based on evidence theory. It differs completely from other multimodel techniques in its mathematical foundation and how it provides the quantitative assessment of the simulation uncertainty. The approach allows one to combine individual solutions produced by different models along with the quantified information on the past performance of the models.

How one links the tools of evidence theory to a real-life problem strongly depends on the problem. Previously, we formulated and successfully tested the multimodel algorithm for subsonic turbulent flow simulations [1] and hurricane track forecasts [2]. The general formulation of the algorithm is provided in the current paper. Following the steps described, one can apply the algorithm to any problem that involves different modelling alternatives and has appropriate data.

1

S.V. Poroseva, M.Y. Hussaini, S.L. Woodruff, "On Improving the Predictive Capability of Turbulence Models Using Evidence Theory", AIAA J., 44(6), 1220-1228, 2006. doi:10.2514/1.15756

2

S.V. Poroseva, J. Letschert, M.Y. Hussaini, "Application of Evidence Theory to Quantify Uncertainty in Hurricane/Typhoon Tracks Forecasts", Meteorology and Atmospheric Physics, Special issue on tropical cyclones, 97, 149-169, 2007.

3

G. Shafer, "A Mathematical Theory of Evidence", Princeton, NJ: Princeton University Press, 1976.

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