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 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.
Highlights
Models are often used to describe biological systems, for which parameters are often considered as fixed constants [1,2]
The main objective of uncertainty quantification (UQ) is to study the impact of uncertainty on model predictions [1,3,4,5,6], which is vital to assess the trustworthiness of model predictions for process design and performance evaluation [2,4,7,8]
We have developed an algorithm to convert a high-dimensional integral in stochastic Galerkin (SG) into a few lower-dimensional ones [20,21], using the generalized dimension reduction method [22]
Summary
Models are often used to describe biological systems, for which parameters are often considered as fixed constants [1,2]. While the efficiency of the SG-based UQ was verified in several applications in terms of UQ accuracy and computational time [14,15,16,18,19], the calculation of PCE coefficients with the SG projection can be challenging, especially when the model involves many uncertainties and nonpolynomial terms [10,17] In this case, it may be computationally prohibitive to compute the PCE coefficients of model predictions, especially when evaluating high-dimensional integrals is required. The most popular technique to generate collocation points is the full tensor product (NIDP-FT) but as the number of uncertainties increases, the total number of required collocation points grows significantly This increases the computational time to compute the PCE coefficients of model predictions, which is recognized as the curse of dimensionality [10,25].
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