Detection of probability distribution and regimes in nonlinear systems with nonlinear dimension reduction methods

使用非线性降维方法检测非线性系统中的概率分布和状态

• 批准号: 21740344
• 负责人: NISHIZAWA Seiya
• 金额: $ 2.66万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740344/
• 关键词: 非線形次元削減; 確率分布; レジーム; 非線形システム

The atmospheric system is a high dimensional nonlinear system and naive analyses of variability in the system is not easy due to the high dimensionality. In this study, I extract low dimensional manifolds from strongly nonlinear atmospheric variability, such as temperature in winter polar stratosphere and precipitation, with nonlinear dimension reduction methods. Those manifolds show asymmetry in physical quantities between positive and negative values, although the asymmetry cannot be represented with linear methods. Additionally I estimate existence probability distribution of state variables and clusters on the manifolds, and obtain possible regimes, though it is not statistically significant.

大气系统是一个高维的非线性系统，由于其高维性，对系统的变率进行简单的分析是不容易的。在这项研究中，我提取低维流形的强非线性大气变率，如冬季极地平流层温度和降水，非线性降维方法。这些流形在物理量的正负之间表现出不对称性，尽管这种不对称性不能用线性方法来表示。此外，估计了流形上状态变量和簇的存在概率分布，并得到了可能的制度，虽然它不是统计上显著的。