Prof. Guillaume Bonnet (University of California Santa Barbara)

Title: Nonlinear Stochastic PDEs for Highway Traffic Flows: Theory and Calibration to Traffic Data

Abstract: Highway traffic flows are generally modeled by partial differential equations (PDEs). These models are used by traffic engineers for road design, planning or management. However, they often fail to capture important features of empirical traffic flow studies, particularly at
small scales. In this talk, I will propose a fairly simple stochastic model in the form of a nonlinear stochastic partial differential equation(SPDE) with random coefficients driven by a Poisson random measure. I will discuss the well posedness of the proposed equation as well as the corresponding inverse problem that I will illustrate by its calibration to high resolution traffic data from highway 101 in Los Angeles.