"This proposal is aimed at developing and analyzing a fundamentally new interdisciplinary approach for the modeling, simulation, control and optimization of multi-physics, multi-scale dynamical systems. The new innovative feature is to generate models via a network of modularized uni-physics components, where each component incorporates a mathematical model for the dynamical behavior as well as a model for the uncertainties, e.g. due to modeling, discretization or finite precision computation errors. Based on this new modeling concept also new numerical simulation, control, and optimization techniques will be developed and incorporated, that allow a systematic adaptive error control (including the appropriate treatment of different scales,and the uncertainties) for the components as well as for the whole multi-physics model. In order to cope with the differential-algebraic and multi-scale character of the systems we will develop and analyze remodeling techniques for the components as well as for the whole network including the uncertainties and special structures. The new remodeled systems will be designed such that they allow an efficient and accurate dynamical simulation with high order numerical integration techniques as well as efficient methods for model reduction and open and closed loop control.In an interdisciplinary corporation with colleagues from computer science and engineering we will extend the modeling language MODELICA to be able to incorporate the new features (in particular the uncertainties and modeling errors) and we also plan to implement the complete approach as a new software platform."