Title: Exploring uncertainty in traffic flow models
Abstract: In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world systems. Uncertainty can be addressed using intrusive methods, such as the stochastic Galerkin approach, which modify the governing equations, or non-intrusive methods, like Monte Carlo and stochastic collocation, which rely on deterministic solvers applied to sampled scenarios.
In this talk, we mainly deal with non-intrusive techniques, in particular strategies for handling high-dimensional problems using control variate approaches, including multi-level and multi-fidelity Monte Carlo methods. Here, accurate models provide high-fidelity representations but require high computational cost, while simplified models, as low-fidelity surrogates, offer approximate solutions at a lower computational cost. Numerical simulations show that the multi-fidelity approach offers significant accuracy improvements over standard Monte Carlo methods.
This is a joint work with M. Herty and L. Pareschi.