Overview on SFB Sparsity and Singular Structures

Our research center is concerned with the mathematical foundations for computational approaches in machine learning, signal processing and simulation. The concept of sparsity, understood in a broad sense, is crucial in these fields. We investigate the mathematics of sparsity-based method, of singular structures in PDEs and interactions between these area. We focus on relevant aspects in numerical analysis, analysis of PDEs, mathematical foundations of machine learning and signal processing, discrete and continuous optimization, probability theory and computational algebra.

The research within our collaborative research center is concerned with several core topics:

  • Sparsity representations
  • Low rank matrices and tensors
  • Deep neural networks
  • Singular functions and fields
  • Order reduction and effective models
  • Gradient flows and (stochastic) gradient descent
  • Low-dimensional manifolds and geodesics
  • Parametric equations
  • Group theory and symmetries
  • Kinetic equations

The CRC is devided into three project groups

A Data Processing
B Kinetic and Parametric Models
C Singular and Geometric PDEs