Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems
Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems
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DOI：
10.3390/applmech1030011
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发表时间：
2020-08
影响因子：
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通讯作者：
Jeongeun Son;D. Du;Yuncheng Du
中科院分区：
文献类型：
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作者：
Jeongeun Son;D. Du;Yuncheng Du
不确定性量化（UQ）是数学建模与仿真的重要组成部分，它量化了参数不确定性对模型预测的影响。提出了一种基于多项式混沌展开（PCE）的生物系统UQ方法。对于PCE，关键的一步是随机Galerkin（SG）投影，它产生一个家庭的PCE系数的确定性模型来描述原始的随机系统。当处理涉及非多项式项和许多不确定性的系统时，基于SG的PCE在计算上是禁止的，因为它通常涉及高维积分。为了解决这个问题，广义降维方法（gDRM）与求积规则相结合，将SG中的高维积分转换为一些可以快速求解的低维积分。通过两个描述细胞动态行为的例子验证了算法的性能。与其他UQ技术（例如，非侵入性PCE），结果显示了该算法在更复杂的生物系统中解决UQ的潜力。
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.