WIAS Research Highlights

Inverse problems are ubiquitous in all areas of science where measurements and data play a role. We focus on mathematical foundations for applications as magnetic resonance imaging (MRI) and quantitative MRI (qMRI).

Transferring important physical properties from a continuous model to a discrete version of this model is of utmost importance for various applications. We develop, analyze, and apply physically consistent discretizations.

Gels are versatile materials that combine physical properties of liquids and solids. We bridge microscopic stochastic particle interpretation with the macroscopic continuum representation of materials, working towards a unified understanding of gelation.

Research results are highlighted that have been achieved with the goal of formulating of a general mathematical structure that supports the mathematical modeling and analysis of processes with bulk-interface coupling in a variational framework

We developed a numerical tool capable of efficiently constructing and solving the spectral problem for PCSELs. Simulations and analysis of the field coupling matrix and calculated spectra led us to identify a special feature.

We deal with phase transitions arising from random graphs occurring in diverse contexts. The models we consider reflect many real-world properties, such as clustering and being scale free, and often exhibit important features associated with the networks.

Electron shuttling devices are new functional elements in modular concepts for spin-qubit based quantum computers that have promising prospects for scalability due to direct compatibility with industrial fabrication techniques. Numerical device simulation is crucial for understanding limitions.

Convolutional neural networks are an efficient tool to solve pPDEs and are amenable to a thorough mathematical analysis. Small approximation errors can be achieved with network sizes growing only logarithmically with the inverse of the required error bound.

We combined mathematical homogenization and stochastic geometry to provide new models and methods for examining random materials, aiming at better understand and model the behavior of systems in random media.

Thermodynamic structures give rise to effective methods to analyze cross-diffusion, including change to entropy variables and symmetrization.