In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during the modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification (UQ) approaches are based on assumptions of stochasticity in real, reciprocal, or functional spaces to make them computationally tractable. This makes the prediction of important quantities of interest, such as rare events, difficult. In this paper, a new approach to capture model-form uncertainty is proposed. It is based on fractional calculus, and its flexibility allows us to model a family of non-Gaussian processes, which provides a more generic description of the physical world. A generalized fractional Fokker–Planck equation (fFPE) is used to describe the drift-diffusion processes under long-range correlations and memory effects. A new model-calibration approach based on the maximum mutual information is proposed to reduce model-form uncertainty, where an optimization procedure is taken.
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September 2016
Research Papers
Model-Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives
Yan Wang
Yan Wang
School of Mechanical Engineering, Georgia Institute of Technology
, Atlanta, GA 30332
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Yan Wang
School of Mechanical Engineering, Georgia Institute of Technology
, Atlanta, GA 30332
Manuscript received July 13, 2015; final manuscript received November 19, 2015; published online July 1, 2016. Assoc. Editor: Ioannis Kougioumtzoglou.
ASME J. Risk Uncertainty Part B. Sep 2016, 2(3): 031006 (9 pages)
Published Online: July 1, 2016
Article history
Received:
July 13, 2015
Revision Received:
November 19, 2015
Accepted:
November 20, 2015
Citation
Wang, Y. (July 1, 2016). "Model-Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives." ASME. ASME J. Risk Uncertainty Part B. September 2016; 2(3): 031006. https://doi.org/10.1115/1.4032312
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