基于多保真度蒙特卡洛和多项式混沌展开的颈动脉血流动力学全局敏感性分析
Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for carotid artery haemodynamics
AI总结：
针对心血管计算模型敏感性分析成本高的问题，提出利用 Multifidelity Monte Carlo 估计器结合三维流固耦合与降阶模型，在相同预算下实现更优方差缩减，并对比了 polynomial chaos expansion 的计算成本优势。
摘要：
心血管系统的计算模型越来越多地用于心血管疾病的诊断、治疗和预防。在用于转化应用之前，这些模型的预测能力需要通过验证、确认和不确定性量化来彻底证明。当结果依赖于多个不确定输入时，敏感性分析通常是区分相关输入和不重要输入所需的第一步，并且是确定问题维度初始缩减的关键，这将显著影响所有下游分析任务的成本。对于具有众多不确定输入的计算昂贵模型，基于样本的敏感性分析可能变得不切实际，因为它通常需要大量的模型评估。为了克服这一限制，我们考虑了最近提出的用于 Sobol' 敏感性指数的 Multifidelity Monte Carlo 估计器，并展示了它们在颈总动脉理想化模型中的适用性。通过将少量三维流固耦合模拟与可负担的一维和零维降阶模型相结合，实现了方差缩减。将这些 Multifidelity Monte Carlo 估计器与传统 Monte Carlo 和 polynomial chaos expansion 估计进行了比较。具体而言，我们展示了双保真度（1D/0D）和三保真度（3D/1D/0D）估计器一致的敏感性排名，并且在相同计算预算下，与传统的单保真度 Monte Carlo 估计器相比具有更优的方差缩减。由于 Sobol' 指数的 Monte Carlo 估计器的计算负担受问题维度的影响很大，因此发现 polynomial chaos expansion 对于具有平滑随机响应的理想化模型具有更低的计算成本。
英文摘要：
Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample-based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three-dimensional fluid-structure interaction simulations with affordable one- and zero-dimensional reduced order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi- (1D/0D) and tri-fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single-fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.
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