Multilevel sparse tensor product approximation for manifolds and for functions and operators on manifolds (C04)

流形以及流形上的函数和运算符的多级稀疏张量积近似 (C04)

• 批准号: 233527731
• 金额: --
• 依托单位: Institut für Numerische Simulation
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/233527731?language=en
• 关键词: Multilevel; sparse; tensor; product; approximation

In many high-dimensional applications observed data stem from a low-dimensional submanifold of the high-dimensional ambient space. In this project, we devise novel methods to detect the intrinsic structure of this manifold in order to circumvent the curse of dimensionality, which dooms any classical numerical approximation. We combine several nonlinear approximation steps to identify processes which emerge from the high-dimensional input data. This will allow the treatment of regression problems and PDEs on manifolds in a cost-efficient way.

在许多高维应用中，观察到的数据源自高维环境空间的低维子流形。在这个项目中，我们设计了新的方法来检测该流形的内在结构，以规避维数灾难，维数灾难注定了任何经典的数值近似。我们结合几个非线性近似步骤来识别从高维输入数据中出现的过程。这将允许以经济高效的方式处理流形上的回归问题和偏微分方程。