Alexandra Würth (INRIA) - Data Science
Date: - Location: Eurecom
Abstract: We ([2]) propose a Bayesian calibration technique for parameter identification and uncertainty quantification in macroscopic traffic flow models, exploiting different loop detector data sets. We validate the results comparing the error metrics of both first and second order models. While needing more parameter calibration, second order models generally perform better in reconstructing traffic quantities of interest. Macroscopic traffic flow models have been employed for decades to describe the spatio-temporal evolution of aggregate traffic quantities such as density and mean velocity. Classically, macroscopic traffic models are calibrated either by fitting the so-called fundamental diagram (i.e., the density-flow or density-speed mapping described by the model flux function) or by minimizing some error measure of the simulation output. The calibration can be done against either data provided by loop detectors at fixed locations or trajectory data. To our knowledge however, few works have been devoted evaluating the uncertainty of both models and data. Thus, we propose to follow a Bayesian approach, which allows us to evaluate the parameter probability distribution given the observed data. Moreover, following Kennedy-O’Hagan [1], we introduce a bias term to better account for possible discrepancies between the mathematical models and reality; this bias term is modeled by a Gaussian process. [1] M. C. Kennedy and A. O’Hagan. Bayesian calibration of computer models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(3): 425-464, 2001. [2] A. Würth, M. Binois, P. Goatin and S. G ¨ottlich. Data driven uncertainty quantification in macroscopic traffic flow models. submitted, 2021. Short bio: Alexandra Würth is a PhD student, supervised by Paola Goatin and Mickaël Binois, at INRIA Sophia Antipolis Méditerranée in the ACUMES Project Team since February 2021. Her subject, “AI for road traffic modeling and management “, aims to analyse information derived from traffic data using different statistical methods and exploiting them within deterministic PDE models. In October 2020, Alexandra received her Master’s degree (M.Sc.) at the University of Mannheim, Germany, in Business Mathematics with focus on numerical methods for hyperbolic conservation laws. The master thesis, with its title “First and second order traffic flow model calibration by statistical approaches”, was coupled with an internship at INRIA from April 2020 – September 2020. Data Science Seminars: https://ds.eurecom.fr/seminars/ https://mediaserver.eurecom.fr/channels/#data-science-seminars (internal)
