Numerical Methods for Stochastic Partial Differential Equations and Its Application in Complex Biological and Environmental Systems
发布者：系统管理员发布时间：2013-07-23浏览次数：1803
| 报告题目： | Numerical Methods for Stochastic Partial Differential Equations and Its Application in Complex Biological and Environmental Systems |
| 报 告 人： | 林光 研究员 |
| | Pacific Northwest National Laboratory |
| 报告时间： | 7月25日上午9:30-10:30 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in modeling, simulation and optimization of complex systems. In this talk, a new formulation for analyzing uncertainty sensitivity, quantifying uncertainty and visualizing uncertainty will be discussed. An integrated simulation framework will be presented that quantifies both numerical and modeling errors in an effort to establish "error bars" in numerical simulations. In particular, stochastic formulations based on Galerkin and collocation versions of the generalized Polynomial Chaos (gPC) will be discussed. Additionally, we will present some effective new ways of dealing with this "curse of dimensionality". Particularly, adaptive ANOVA decomposition, some stochastic sensitivity analysis, selection of polynomial chaos bases via Bayesian model uncertainty methods will be discussed in some detail. Several specific examples on sensitivity analysis and predictive modeling of thrombin production in blood coagulation chemical reaction network, flow and transport in randomly heterogeneous porous media, random roughness problem, and uncertainty quantification in climate modeling will be presented to illustrate the main idea of our approach. |
