Investigating Uncertainty in Traffic Flow Modeling - Multi-Level Monte Carlo and Multi-Fidelity Approaches

Explore advanced mathematical approaches for modeling uncertainty in traffic flow systems through this 42-minute conference talk. Delve into the critical role of partial differential equations (PDEs) in describing traffic dynamics, including density, speed, and flux patterns across time and space. Examine how real-world uncertainties from fluctuating demand, unpredictable incidents, and varying driver behaviors impact model accuracy and reliability. Learn about non-intrusive uncertainty quantification methods, specifically focusing on multi-fidelity control variate methods and multi-level Monte Carlo approaches. Discover how multi-fidelity methods exploit the multiscale nature of traffic problems by combining high-fidelity kinetic models with computationally efficient macroscopic models to reduce variance in Monte Carlo simulations. Understand the multi-level Monte Carlo technique that balances simulations across different accuracy levels, using inexpensive coarse simulations for broad trends while employing fine simulations for error correction. Analyze numerical simulation results demonstrating significant accuracy improvements compared to standard Monte Carlo methods while maintaining manageable computational costs. Gain insights into how these advanced mathematical frameworks enhance model reliability and support the development of more effective traffic management solutions and infrastructure improvements.