Application Areas

The MATH+ Application Areas are tailored toward mathematical research in interdisciplinary application fields. They support cross-institution research projects that involve mathematicians as well as leading experts of the respective field of application. The following list displays the research projects presently running in the four Application Areas. Successfully completed projects can be found on the subsequent websites of the individual Application Areas.

Projects marked with an asterisk (*) are short-term one-year pilot projects.

Mechanisms of Life (AA1)
Scientists in Charge: Edda Klipp, Frank Noé, Christof Schütte

• AA1-6: Data-Driven Modeling from Atoms to Cells
  Frank Noé, Cecilia Clementi, Christof Schütte
• AA1-8: Random Bifurcations in Chemical Reaction Networks
  Maximilian Engel
• AA1-10: New Methods for Inhibiting Sars-Cov2 Cell Entry
  Frank Noé, Oliver Daumke
• AA1-14: Development of an Ion-Channel Model-Framework for In-vitro Assisted Interpretation of Current Voltage Relations
  Jürgen Fuhrmann, Manuel Landstorfer, Barbara Wagner
• AA1-15: Math-Powered Drug-Design
  Konstantin Fackeldey, Christof Schütte, Vikram Sunkara, Christoph Stein, Marcus Weber, Stefanie Winkelmann
• AA1-16: Spatial Dynamics of Cell Signalling Explored with Agent-Based Modeling
  Edda Klipp, Rune Linding, Caren Tischendorf
• AA1-17: Beyond Attractors: Understanding the Transient and Modular Behaviour of Boolean Networks
  Elisa Tonello
• AA1-18: Synchronization and Geometric Structures of Stochastic Biochemical Oscillators
  Maximilian Engel, Felix Höfling, Stefanie Winkelmann

Successfully completed projects of Application Area 1 can be found here.

Nano and Quantum Technologies (AA2)
Scientists in Charge: Uwe Bandelow, Ralf Kornhuber, Barbara Zwicknagl

• AA2-7: Sparse Deep Neuronal Networks for the Design of Solar Energy Materials
  Andrea Walther, Stephan Schmidt, Bernd Rech, Eva Unger
• AA2-8: Deep Backflow for Accurate Solution of the Electronic Schrödinger Equation
  Jan Hermann, Jens Eisert, Frank Noé
• AA2-12: Nonlinear Electrokinetics in Anisotropic Microfluids – Analysis, Simulation, and Optimal Control
  Etienne Emmrich, Dietmar Hömberg, Robert Lasarzik
• AA2-13: Data-Driven Stochastic Modeling of Semiconductor Lasers
  Uwe Bandelow, Markus Kantner, Wilhelm Stannat, Hans Wenzel
• AA2-16: Tailored Entangled Photon Sources for Quantum Technology
  Sven Burger, Stephan Reitzenstein
• AA2-17: Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
  Tobias Breiten, Markus Kantner, Thomas Koprucki
• AA2-18: Pareto-Optimal Control of Quantum Thermal Devices with Deep Reinforcement Learning
  Paolo Erdman

Successfully completed projects of Application Area 2 can be found here.

Next Generation Networks (AA3)
Scientists in Charge: Ralf Borndörfer, Martin Skutella

• AA3-2: Nash Flows over Time in Transport and Evacuation Simulation
  Kai Nagel, Martin Skutella
• AA3-9: Information Design for Bayesian Networks
  Max Klimm
• AA3-12: On the Expressivity of Neural Networks
  Christian Haase, Martin Skutella
• AA3-13: Placing Steiner Points in Constrained Tetrahedrelizations
  Marc Alexa, Hang Si
• AA3-14: The Structure within Disordered Cellular Materials
  Myfanwy Evans, Francisco Garcia-Moreno, Frank Lutz, John Sullivan
• AA3-15: Convex Solver Adaptivity for Mixed-Integer Optimization
  Mathieu Besançon, Ralf Borndörfer, Sebastian Pokutta
• AA3-16: Likelihood Geometry of Max-Linear Bayesian Networks
  Carlos Enrique Améndola Cerón

Successfully completed projects of Application Area 3 can be found here.

Energy Transition (AA4)
Scientists in Charge: Peter Karl Friz, René Henrion, Caren Tischendorf

• AA4-2: Optimal Control in Energy Markets Using Rough Analysis and Deep Networks
  Christian Bayer, Peter Karl Friz, John Schoenmakers, Vladimir Spokoiny
• AA4-7: Decision-Making for Energy Network Dynamics
  Falk Hante, Michael Hintermüller, Sebastian Pokutta
• AA4-8: Recovery of Battery Ageing Dynamics with Multiple Timescales
  Martin Eigel, Martin Heida, Manuel Landstorfer
• AA4-9: Volatile Electricity Markets and Battery Storage: A Model-Based Approach for Optimal Control
  Christian Bayer, Dörte Kreher, Manuel Landstorfer
• AA4-10: Modelling and Optimization of Weakly Coupled Minigrids under Uncertainty
  René Henrion, Dietmar Hömberg
• AA4-11: Using Mathematical Programming to Enhance Multiobjective Learning
  Aswin Kannan
• AA4-12: Advanced Modeling, Simulation, and Optimization of Large Scale Multi-Energy Systems
  Volker Mehrmann
• AA4-13: Equilibria for Distributed Multi-Modal Energy Systems under Uncertainty
  Pavel Dvurechenskii, Caroline Geiersbach, Michael Hintermüller, Aswin Kannan

Successfully completed projects of Application Area 4 can be found here.

Variational Problems in Data-Driven Applications (AA5)
Scientists in Charge: Michael Hintermüller, Sebastian Pokutta

AA5 evolved from a merger of selected projects of the Emerging Fields Extracting Dynamical Laws from Complex Data (EF1) and Model-Based Imaging (EF3).

• AA5-1: Sparsity and Sample-Size Efficiency in Structured Learning
  Sebastian Pokutta
• AA5-2: Robust Multilevel Training of Artificial Neural Networks
  Michael Hintermüller, Carsten Gräser
• AA5-3: Manifold-Valued Graph Neural Networks
  Christoph von Tycowicz, Gabriele Steidl
• AA5-4: Bayesian Optimization and Inference for Deep Networks
  Claudia Schillings, Vladimir Spokoiny
• AA5-5: Wasserstein Gradient Flows for Generalised Transport in Bayesian Inversion
  Martin Eigel, Claudia Schillings, Gabriele Steidl
• AA5-6: Convolutional Proximal Neural Networks for Solving Inverse Problems
  Gabriele Steidl, Andrea Walther
• AA5-7: Integrated Learning and Variational Methods for Quantitative Dynamic Imaging
  Michael Hintermüller, Christoph Kolbitsch, Tobias Schäffter