不确定性量化的自适应方法及其在环境科学中的应用

Uncertainty quantification (UQ) has been a hot research topic recently. UQ has a variety of applications, including hydrology, fluid mechanics, data assimilation, and weather forecasting. High order UQ numerical methods have become one of the important tools; and the relevant computational techniques and their mathematical theory have attracted great attention in recent years. In this project, we shall focus on the developments of high order UQ methods, and in particular, we shall try to design and analyze the adaptive stochastic collocation methods. Furthermore, the project will pursue collaboration between the mathematics department and the environmental department to develop UQ methods for environmental applications such as the subsurface flow simulation and the climate forecasting models.

不确定性量化是近年来国际热门的研究领域，其应用领域包括水文学，流体力学，数据同化，气候预测等。相关的高精度算法理论引起了极大关注。本项目致力于不确定性量化的高精度算法研究，特别的，我们致力于设计与分析自适应随机配置方法。并且，本项目将联合数学系与环境学院，尝试不确定性量化方法在地下水模型和气候模型中的应用。

在项目执行期间，项目组成员按着既定研究目标，在不确定性量化等多个研究课题取得若干研究进展，如不确定性量化的最优抽样算法、贝叶斯反问题的自适应替代模型方法、不确定性量化的机器学习算法等。此外，课题组还在时间分数阶相场模型、时间并行算法、正倒向随机微分方程等多个研究课题取得重要进展。项目组共发表国际权威期刊发表论文40余篇，包括SIAM Review，SIAM J. Numer. Analy.等，相关研究成果有望在不确定性分析中发挥重要作用。