Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models.

中文翻译：

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用多级和准蒙特卡罗对脑间质液中示踪剂分布的快速不确定性量化

有效的不确定性量化算法是了解不确定性传播的关键——从不确定的输入参数到不确定的输出量——在大脑生理学的高分辨率数学模型中。准蒙特卡罗 (QMC) 和多级蒙特卡罗 (MLMC) 等高级蒙特卡罗方法有可能显着改进标准蒙特卡罗 (MC) 方法，但它们在生物医学应用中的适用性和性能尚未得到充分探索。在本文中，我们设计并应用 QMC 和 MLMC 方法来量化大脑内示踪剂传输的对流扩散模型中的不确定性。我们表明，当随机输入的数量很少时，QMC 优于标准 MC 模拟。