Probabilistic numerical methods for Inverse Problems

反问题的概率数值方法

• 批准号: 2437932
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2437932
• 关键词: Probabilistic; numerical; methods; Inverse; Problems

This project is concerned with numerical methods for function spaces that would possibly include applications to inverse problems. In particular, probabilistic methods for function spaces provide us with a mathematical framework to define relationships between quantities of interest and our observed data. Because the relationships are probabilistic, it also enables us to make inferences on the quantities in a probabilistic manner. A good example of an inverse problem is determining material properties of a structure by looking at a satellite image. In its nature, the problem is very ill-defined, e.g. the solutions are unstable with respect to the data or not unique. For such problems, we need to find ways to define and characterize function spaces and to be able to learn from noisy and limited data. This mathematical theory is fundamental for the ongoing development of methods to solve such ill-posed problems.

该项目涉及函数空间的数值方法，可能包括反问题的应用。特别是，函数空间的概率方法为我们提供了一个数学框架来定义感兴趣的数量和我们观察到的数据之间的关系。因为这些关系是概率性的，所以它也使我们能够以概率的方式对数量进行推断。反演问题的一个很好的例子是通过查看卫星图像来确定结构的材料属性。从本质上讲，这个问题是非常不明确的，例如解决方案就数据而言不稳定或不唯一。对于此类问题，我们需要找到定义和表征函数空间的方法，并能够从嘈杂和有限的数据中学习。这种数学理论对于不断开发解决此类不适定问题的方法至关重要。