The project work concentrates on modeling aspects as well as the conception and analysis of robust numerical methods for solving inverse problems for switching (or hybrid) systems of partial differential equations on graphs. In this context, the graph typically represents a transportation network for a specific substance or commodity. In accordance with the focus application of this collaborative research center (CRC), the main emphasis lies on networks transporting for (natural) gas. The project pursues several research goals:
- The identification of unknown parameters (e.g. the Darcy friction factor) and the detection of anomalies (leakage).
- the optimal arrangement of sensors in the network for a robustifying the identification tasks
- the quantification of uncertainties in the identified parameters or in other statistically relevant quantities.
Within the CRC, this project will collaborate with other subprojects on (constrained) optimal control problems for hyperbolic or hybrid systems and their numerical realization, and on numerical methods for the identification of the friction coefficient. It will equip the hierarchy of models considered with the CRC with relevant physical parameters or statistical information resulting from solving various identification problems. The project participates in demonstrator D1.
A poster to B02 can be found here.