Model Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives

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Corresponding author.

Manuscript received July 13, 2015; final manuscript received November 19, 2015; published online Month XX, XXXX. Assoc. Editor: Ioannis Kougioumtzoglou.

ASME doi:10.1115/1.4032312 History: Received July 13, 2015; Revised November 19, 2015


In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification 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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