Abstract
We apply the Koopman operator framework to pedestrian dynamics. In an example scenario, we generate crowd density time series data with a microscopic pedestrian simulator. We then approximate the Koopman operator in matrix form through Extended Dynamic Mode Decomposition, using Geometric Harmonics on the data as a dictionary. The Koopman matrix is integrated into a surrogate model, which allows to approximate crowd density time series data to be generated, independently from the original microscopic simulator. The evaluation of the constructed surrogate model is orders of magnitude faster, and enables us to use methods that require many model evaluations.
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Acknowledgments
This work is supported by the German Research Foundation (DFG) grant no. KO 5257/3-1. The work of I.G.K. was partially supported by the DARPA PAI program. D.L. thanks the research office (FORWIN) of Munich University of Applied Sciences and the Faculty Graduate Center CeDoSIA of TUM Graduate School at Technical University of Munich for their support.
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Lehmberg, D., Dietrich, F., Kevrekidis, I.G., Bungartz, HJ., Köster, G. (2020). Exploring Koopman Operator Based Surrogate Models—Accelerating the Analysis of Critical Pedestrian Densities. In: Zuriguel, I., Garcimartin, A., Cruz, R. (eds) Traffic and Granular Flow 2019. Springer Proceedings in Physics, vol 252. Springer, Cham. https://doi.org/10.1007/978-3-030-55973-1_19
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