Quantifying uncertainty: innovations in high dimensional computation

高维问题（其中有数百或数千个连续变量的问题）出现在许多应用中，从地下水流到数学物理和金融。它们通常对计算资源提出重大挑战，并在设计新的和改进的方法以及证明它们是有效的方面提出严重的数学挑战。这个项目的目的是为高维问题发展新的计算方法和理论，并将这些方法应用于重要的应用。预计这些结果将使人们能够更快、更准确地解决日益重要的问题。

High dimensional problems (problems in which there are hundreds or thousands of continuous variables) arise in many applications, from ground water flow to mathematical physics and finance. They typically present major challenges to computational resources and serious mathematical challenges in devising new and improved methods and in proving that they are effective. The aim of this project is to develop new computational methods and theory for high dimensional problems, and to apply these methods to significant applications. The results are expected to allow faster and more accurate solution of problems of growing importance.