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

• Subject Area: Mathematics
• Term: since 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 211504053

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.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1060: The Mathematics of Emergent Effects
• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Project Head: Professor Dr. Michael Griebel