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【北航数学论坛】Method of Distributions for Hyperbolic Conservation Laws with Random Inputs
ag平台网址:2019-11-19  浏览量:

报告题目Method of Distributions for Hyperbolic Conservation Laws with Random Inputs  

报告人Daniel Tartakovsky教授

报告人单位: 斯坦福大学

报告时间:20191127日下午 1400-1500    

报告地点:沙河主楼404    

摘要Parametric uncertainty, considered broadly to include uncertainty in system parameters and driving forces (source terms and initial and boundary conditions), is ubiquitous in mathematical modeling. The method of distributions, which comprises PDF and CDF methods, quantifies parametric uncertainty by deriving deterministic equations for either probability density function (PDF) or cumulative distribution function (CDF) of model outputs. Since it does not rely on finite-term approximations (e.g., a truncated Karhunen-Loeve transformation) of random parameter fields, the method of distributions does not suffer from the ``curse of dimensionality''. On the contrary, it is exact for a class of nonlinear  hyperbolic equations whose coefficients lack spatio-temporal correlation, i.e., exhibit an infinite number of random dimensions. In settings that require a closure approximation, we use of neural networks to learn the coefficients in the CDF equations from a training set of Monte Carlo runs.

报告人概况: Daniel Tartakovsky教授本科毕业于前苏联喀山州立大学应用数学与力学系,在1993-1996年师从于美国工程院院士Sholom Neuman博士,并于1996年获得了亚利桑那大学的博士学位。他随后加入了美国能源部洛斯阿拉莫斯国家实验室数学建模与分析小组,并先后担任了博士后研究员、小组负责人等职位。Tartakovsky教授2004年加入加州大学圣地亚哥分校,并于2008年获得了终身正教授。2016年,他接受了斯坦福大学能源与环境ag平台app下载的终身教授职位,一直工作至今。Tartakovsky教授的主要研究兴趣是应用数学、计算数学的理论及其在环境流体和生物医学建模中的应用。他先后在PNASSIAMJournal of Fluid Mechanics, Physical Review Letters 等著名期刊上发表了175篇文章,总引用为5083.    

邀请人:王鹏
 

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