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

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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.