Adaptive Numerical Algorithms for Forward UQ in Time-Dependent PDEs

瞬态偏微分方程中正向 UQ 的自适应数值算法

• 批准号: 2332333
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2332333
• 关键词: Adaptive; Numerical; Algorithms; Forward; UQ

Uncertainty quantification (UQ) is a rapidly-evolving field, incorporating several traditional mathematical disciplines. This project will develop new adaptive numerical algorithms for the forward propagation of uncertainty in time-dependent CFD (computational fluid dynamics) models.When we use mathematical models to simulate real-world processes (such as fluid flows) we frequently encounter situations where we are uncertain about one or more of the inputs (viscosity, material parameters, initial conditions, geometry etc). In forward UQ, the main aim is to assess the impact of uncertainty in the model inputs on quantities of interest associated with the model's outputs. For this, we require computationally efficient numerical methods that can take in a probability distribution for the model's inputs and deliver accurate approximations of statistical quantities of interest related to the model's outputs. For time-dependent problems, and especially those with non-smooth solutions, the approximation space often needs to be adapted in time to maintain accuracy. How to design adaptive numerical algorithms with guaranteed error control is highly challenging. This project is a numerical analysis project that will develop new adaptive numerical schemes for forward UQ driven by rigorous error estimation.

不确定性量化（UQ）是一个快速发展的领域，融合了几个传统的数学学科。该项目将开发新的自适应数值算法，用于时变CFD（计算流体动力学）模型中不确定性的前向传播。当我们使用数学模型来模拟现实世界的过程（如流体流动）时，我们经常遇到一个或多个输入（粘度、材料参数、初始条件、几何形状等）不确定的情况。在前向UQ中，主要目的是评估模型输入中的不确定性对与模型输出相关的兴趣量的影响。为此，我们需要计算效率高的数值方法，这些方法可以接受模型输入的概率分布，并提供与模型输出相关的统计量的精确近似值。对于时变问题，特别是具有非光滑解的问题，往往需要及时调整逼近空间以保持精度。如何设计保证误差控制的自适应数值算法是一个非常具有挑战性的问题。该项目是一个数值分析项目，将开发新的自适应数值方案，以严格的误差估计驱动前向UQ。