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Appl. Mech., Volume 1, Issue 3 (September 2020) – 1 article

Cover Story (view full-size image): Uncertainty quantification (UQ) to quantify the effect of uncertainty on model predictions is essential to improve the accuracy of computational models. The polynomial chaos expansion (PCE), one of the most popular UQ techniques, has gained increasing attention lately. The key to the successful application of PCE is stochastic Galerkin projection, which yields coupled deterministic models of PCE coefficients to describe a stochastic system. However, when a system involves nonpolynomial terms and many uncertainties, it is computationally challenging to solve PCE coefficients. In this work, the PCE and generalized dimension reduction methods were combined with the sampling-based gaussian quadrature rules to quickly calculate the PCE coefficients, and the efficiency of the algorithm was demonstrated with examples of biological systems. View this paper
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21 pages, 2415 KiB  
Article
Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems
by Jeongeun Son, Dongping Du and Yuncheng Du
Appl. Mech. 2020, 1(3), 153-173; https://doi.org/10.3390/applmech1030011 - 22 Aug 2020
Cited by 4 | Viewed by 4034
Abstract
Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key [...] Read more.
Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive because it often involves high-dimensional integrals. To address this, a generalized dimension reduction method (gDRM) is coupled with quadrature rules to convert a high-dimensional integral in the SG into a few lower dimensional ones that can be rapidly solved. The performance of the algorithm is validated with two examples describing the dynamic behavior of cells. Compared to other UQ techniques (e.g., nonintrusive PCE), the results show the potential of the algorithm to tackle UQ in more complicated biological systems. Full article
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