基于加权近似Fekete点的多项式混沌不确定性量化和敏感性分析的有效采样
Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points
摘要：
在开发患者特异性生理模型时，执行不确定性量化（UQ）和敏感性分析（SA）是至关重要的，因为它可以量化模型输出不确定性并估计模型的每个输入参数对数学模型的影响。通过提供这些信息，UQ和SA作为诊断工具来评估模型的保真度，并将模型特征与专家知识和真实世界的观察结果进行比较。计算效率是UQ和SA方法的重要组成部分，因此优化是一个活跃的研究领域。在这项工作中，我们研究了一种新的有效的最小二乘多项式逼近的采样方法，加权近似Fekete点（WAFP）。我们分析了这种方法的性能，通过展示其效用的心血管模型，估计血氧饱和度响应的变化的随机分析。使用WAFP的多项式混沌（PC）扩展在量化不确定性和识别最有影响力的模型输入（包括输入相互作用）方面产生的结果与更标准的蒙特卡罗相似，当对氧合血红蛋白饱和度建模时，使用WAFP的PC扩展要有效得多。这些研究结果表明，使用WAFP的PC扩展量化的不确定性和分析灵敏度的氧合血红蛋白解离反应模型的有用性。应用这些技术可以帮助分析其他相关模型的保真度，为临床应用做准备。
英文摘要：
Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.
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