空间插值的微分几何方法研究

项目名称： 空间插值的微分几何方法研究

项目编号： No.41471338

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 宋敦江

作者单位： 中国科学院科技战略咨询研究院

项目金额： 90万元

中文摘要： 空间插值，也称空间预测、曲面建模，是地理学的基本问题，是许多地理研究首先碰到的问题。高精度曲面建模（High Accuracy Surface Modeling，HASM）方法是我国学者提出的一套原创性的基于曲面论的空间插值方法。针对HASM长期以来忽略的边界值问题、特征信息融合问题等基础理论问题和模型复杂性高带来的版本管理、模型共享困难等技术问题，提出基于微分几何框架下的空间插值方法（Spatial Interpolation based on Differential Geometry, SIDG），解决边界值问题，提取蕴含原始数据中的特征信息，将特征信息融入到空间插值方法，采用工业上和运筹与管理学领域广泛应用的代数建模语言和优化问题求解器，从微分几何的恒等式出发，快速构建空间插值模型，探索高精度空间插值的本质，构建数据集-空间插值方法集-软件模块集,丰富地理学的方法库。

中文关键词： 空间插值；微分几何；特征提取；优化控制；代数建模语言

英文摘要： Spatial interpolation, also called spatial prediction, surface modeling, is a basic problem of geography, is one priority of many geographical problems. High Accuracy Surface Modeling (High Accuracy Surface Modeling, HASM) is a spatial interpolation method which is originally proposed by Chinese scholars. HASM is based on the surface theory. To attack those problems such as the boundary value problems, characteristic information fusion, difficulty in implementing and sharing of HASM method caused by the complexity of HASM and et al, which has long been ignored by the HASM researchers, a new framework for spatial interpolation based on differential geometry theory is proposed, which is named SIDG. Boundary value problem is solved by SIDG, feature information will be extracted from the original data, and will be used intensively in SIDG.Algebraic modelling languages, which is intensively used in industries, operational research and management, will be used in spatial interpolation modelling, many versions of SIDG will be quickly setup, tested and shared, the nature of spatial interpolation based on differential geometry will be explored through the construction of a repository of data-model-module, and a belief in the open source spirit will enrich the method library of geography.

英文关键词： spatial interpolation;differential geometry;feature extraction;optimal control;algebraic modelling language(AML)