Next Article in Journal
Robust Filtering Options for Higher-Order Strain Fields Generated by Digital Image Correlation
Previous Article in Journal
Damage Evaluation of Free-Free Beam Based on Vibration Testing
Article

Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems

1
Department of Chemical & Biomolecular Engineering, Clarkson University, Potsdam, NY 13699, USA
2
Department of Industrial, Manufacturing & Systems Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
Author to whom correspondence should be addressed.
Appl. Mech. 2020, 1(3), 153-173; https://doi.org/10.3390/applmech1030011
Received: 12 May 2020 / Revised: 11 August 2020 / Accepted: 20 August 2020 / Published: 22 August 2020
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. View Full-Text
Keywords: generalized dimension reduction method; polynomial chaos expansion; uncertainty quantification; stochastic ordinary differential equation; high-dimensional uncertainty analysis generalized dimension reduction method; polynomial chaos expansion; uncertainty quantification; stochastic ordinary differential equation; high-dimensional uncertainty analysis
Show Figures

Figure 1

MDPI and ACS Style

Son, J.; Du, D.; Du, Y. Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems. Appl. Mech. 2020, 1, 153-173. https://doi.org/10.3390/applmech1030011

AMA Style

Son J, Du D, Du Y. Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems. Applied Mechanics. 2020; 1(3):153-173. https://doi.org/10.3390/applmech1030011

Chicago/Turabian Style

Son, Jeongeun, Dongping Du, and Yuncheng Du. 2020. "Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems" Applied Mechanics 1, no. 3: 153-173. https://doi.org/10.3390/applmech1030011

Find Other Styles

Article Access Map by Country/Region

1
Back to TopTop