Sparsity and Singular Structures
This new research center will be concerned with the mathematical foundations for computational approaches in machine learning, signal processing and simulation. Despite vast gains in the speed of computers, the deluge of data and complexity of models describing natural and technical phenomena pose fundamental challenges that cannot be surmounted by computational power alone. Two critical fronts for which the time is ripe to make progress are
signal processing and machine learning with huge data sets and;
partial differential equations with singularities such as point defects or interfaces.
Significantly expanding the frontier in these areas requires new insight into the underlying mathematical structure of the problems. While the two mentioned challenges may appear to have little in common, their analysis will benefit from closely related ideas and algorithms, in particular, from those based on sparsity, that is, low complexity structures in high dimensions.
The SFB 1481 combines the expertise of several mathematicians at RWTH Aachen University working in analysis, probability theory, numerical analysis, optimization and algebra and encompasses 17 scientific sub-projects addressing challenging problems in the above mentioned areas.