University of Kaiserslautern-Landau (RPTU)

Modelling - Simulation - Optimisation

Potential area of the research initiative of the state of RLP

Modelling, simulation and optimisation are core fields of applied mathematics that are used - to varying degrees - to solve a wide range of problems in the natural and engineering sciences and, increasingly, in medicine. This often requires a compromise between mathematically well-understood, theoretical approaches and analytically less accessible, more algorithmically motivated methods. The latter sometimes deliver better results in practice or make the problem calculable in the first place. However, theoretically proven statements on the properties of the methods have to be partially replaced by empirical validation. The situation is similar for complex problems that require the coupling of different individual models across scales and domains. The mathematical properties of the resulting overall system are often not immediately apparent.

The aim of MSO is therefore to develop and analyse suitable mathematical methods that can be used to solve complex practical problems, but for which mathematical statements on accuracy and their limits can also be made and recommendations for parameterisation can be formulated. The complexity of some of the simulations under consideration requires methods of high-performance computing. In addition, especially in the field of 3D imaging, massive amounts of data can be generated, the processing of which places special demands on the hardware and software used.

The area of potential brings together the expertise of ten PIs from applied mathematics, both from Kaiserslautern and Landau. In addition, there is a PI from philosophy who wants to establish this new field of research at RPTU as part of the Heisenberg Professorship "Philosophy in Science and Engineering". The consortium is complemented by AIs - mostly from the engineering sciences - who represent the user perspective in MSO. Scientists from the Fraunhofer ITWM are also represented, who will also participate in planned projects and form the bridge to industrial mathematical research.