Uncertainty Quantification for Dynamical Systems in Mobility
Final Report Abstract
The aim of QUEST was to address the robustness of transport systems to examine concrete scenarios. QUEST thus moves in an interdisciplinary field of high social pertinence. Robustness analyses are important because many model parameters – regardless of a validation against empirical data – are fraught with uncertainties. Within the project, we focused on pedestrian systems, which, unlike car traffic, have so far received little attention in research. We looked at dynamic observation variables, such as the density of a crowd at a bottleneck. We expanded structures in the pedestrian simulator Vadere, which was developed in my research group, to establish a method that systematically varies uncertain parameters. The method is also suitable for the creation of data-driven surrogate models that approximate the system behavior of the observation variables for a specific scenario. In this way, we can elegantly bypass computationally intensive evaluations of the underlying simulator. The heart of QUEST came from a collaboration with the group of Yoannis Kevredkidis at Johns Hopkins University, a leading expert on the mathematical theory of the ‘Koopman operator’. Methodological advances were made towards dynamic surrogate models. The Koopman approach not only allows the rapid calculation of a surrogate but also brings structures of the transport system itself to the light. It is thus an approach of explainable AI. Prior to QUEST, no Koopman software that adheres to strict quality standards was freely available to researchers. With ‘datafold’we close this gap. With our software solutions, we examined concrete traffic scenarios and published at relevant scientific conferences or in journals. In two scenarios, we analyzed the effects of uncertainties on the number of people in typical exit situations in public transport. For our practice partners police, we used surrogate models to describe an extremely computationally intensive scenario: the dependence of the length of a demonstration train on the uncertain parameters ‘number of participants’and ‘variance in the running speeds’. In a fourth traffic system, we applied the methodology of the Koopman Operator to real data: We ‘learned’ the traffic patterns of eleven sensors in the city of Melbourne (Australia) robustly from noisy data of several years and calculated precise predictions. Our publications and our software are free and publicly available. Our results are therefore reproducible. The importance has continued to grow due to the pandemic: Where one wants to avoid crowds, one needs good analyses and predictions of pedestrian densities.
Publications
- “Fast and flexible uncertainty quantification through a data-driven surrogate model". In: International Journal for Uncertainty Quantification 8.2 (2018), pp. 175–192
Felix Dietrich, Florian Künzner, Tobias Neckel, Gerta Köster, and Hans-Joachim Bungartz
(See online at https://doi.org/10.1615/Int.J.UncertaintyQuantification.2018021975) - “Exploring Koopman Operator Based Surrogate Models—Accelerating the Analysis of Critical Pedestrian Densities". In: Traffic and Granular Flow, 2019. Vol. 252. Cham: Springer
Daniel Lehmberg, Felix Dietrich, Ioannis G. Kevrekidis, Hans-Joachim Bungartz, and Gerta Köster
(See online at https://doi.org/10.1007/978-3-030-55973-1_19) - “Datafold: datadriven models for point clouds and time series on manifolds". In: Journal of Open Source Software 5.51, 2020, p. 2283
Daniel Lehmberg, Felix Dietrich, Gerta Köster, and Hans-Joachim Bungartz
(See online at https://doi.org/10.21105/joss.02283) - Datafold: representation learning and time series forecasting, 3/2021, In: Quartl Ausgabe 99 — Offizielles Mitteilungsblatt des Kompetenznetzwerks für Technisch-Wissenschaftliches Hoch- und Höchstleistungsrechnen in Bayern (KONWIHR) und der Bavarian Graduate School of Computational Engineering (BGCE), 2021
Daniel Lehmberg and Felix Dietrich
- “Dynamics of a Simulated Demonstration March: An Efficient Sensitivity Analysis". In: Sustainability 13.6, 2021, p. 3455
Simon Rahn, Marion Gödel, Rainer Fischer, and Gerta Köster
(See online at https://doi.org/10.3390/su13063455) - “Modeling Melburnians - Using the Koopman operator to gain insight into crowd dynamics". In: Transportation Research Part C: Emerging Technologies 133, 2021, 103437
Daniel Lehmberg, Felix Dietrich, and Gerta Köster
(See online at https://doi.org/10.1016/j.trc.2021.103437)
