Inverse Multiscale Problems
Prof. Dr. Martin Burger,, Westfälische Wilhelms-Universität Münster
Modern nonlinear science is full of multiscale processes, where the derivation of efficiently computable models poses significant mathematical challenges. In many cases microscopic models are known, but for efficient simulation one needs coarse-grained meso- or macroscopic models. Coarse-graining is also the basis for the solution of inverse problems, which usually arise when one wants to compute quantities that are not directly accessible from indirect observations or when one seeks optimal designs.
In this talk we present some aspects of multiscale modelling and related inverse problems, with applications in the natural sciences (design of semiconductor devices, crystal growth and nucleation, ion transport through channels and nanopores, chemotaxis) and also in socio-economic systems (swarming, price herding, opinion formation).