Uncertainty Quantification for Dynamical Systems in Mobility

• Applicant: Professorin Dr. Gerta Köster
• Subject Area: Traffic and Transport Systems, Intelligent and Automated Traffic
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 374503505

Mobility is an integral part of our modern world. Traffic networks are used for public and individual traffic, to transport humans and goods. Many persons, especially in big cities, move on foot on their way to and from their work places, to shop and to socialize at big events.Efficient traffic as well as the safety of people depends on the system's ability to keep `flowing'. For this, the dynamic system must form stable and efficient equilibria. Achieving this is the foremost goal of traffic planning and, more recently, of event planning. This goal has by no means been reached.In this context, mathematical models have two functions: to explain how unstable phenomena arise and to predict how the system evolves in a way that planning officials obtain options for action. An example for the former function is appearance of congestions from `nowhere'. Reality, as well as so-called predictive models that attempt to forecast reality, are often very complex. A large number of parameters influence the system. Examples are the number of pedestrians but also the geometry and the surroundings. Most often these parameters are not known but must be estimated. The accuracy of this estimation is very limited. This means that the predictive power of a model depends on its robustness. Forecasts of the future can only be made in a range in which both, the real system and the valid model, are stable and display little sensitivity to small disturbances.This project aims at investigating the robustness of traffic systems, above all for pedestrians. This shall be achieved through mathematical models and computer experiments. We seek to identify and explain instabilities and to quantify the effect of disturbances in both stable and unstable regimes. We intend to do this for complex models with a multitude of agents.We plan to combine recent methods from numerics and analysis that have not been employed in safety science nor traffic planning to this point: uncertainty quantification and numerical model construction of dedicated surrogate models. Uncertainty quantification is a young mathematical and numerical discipline that develops methods to systematically find and record uncertainties in a system. This is done not only qualitatively but quantitatively. The type of surrogate models we aim for in this project are tailored to extract the dominant dynamic from a usually high-dimensional system. For this a new, subsequently independent model is constructed from the data that was produced with the original model. The surrogate model can be simulated much faster. Once such a surrogate model has been constructed it can be used to perform the uncertainty quantification of the original system. This opens the opportunity for the engineer to conduct studies that otherwise could only be computed on a high performance computer.

• DFG Programme: Research Grants
• Cooperation Partner: Professor Dr. Hans-Joachim Bungartz