Mathematical Modeling in Systems Simulation deals with the subject area of dynamical systems. Thereby, ordinary differential equations and related modeling methods are considered, which among others also treat differential-algebraic equations. Building on these approaches, the area of hybrid models opens up, in particular dynamic hybrid system modeling. The system simulation uses these mathematical model descriptions and maps them into different simulation environments. Consideration of these simulation environments requires knowledge of numerical simulation and basic programming skills. Apart from the mathematical modeling of this research area, the focus is also on application areas as well as related methods of applied mathematics to study models from technical natural sciences.
In addition to the addressed topics, methods of model-based machine and reinforcement learning are also applied in the field of system simulation. Furthermore, discrete-time and discrete-value model descriptions are used, such as Discrete Event Systems (DEVS), Agent Based Modeling (ABM), Cellular Automata (CA) but also statistical models and time series analysis.
Mathematical modeling in system simulation is a broad research field and combines different areas of applied mathematics to obtain system models and to study their behavior in simulations. The range of topics extends from the theory of the methods to their application in technical, scientific and engineering problems.