Uncertainty Quantification for Kinetic Equations I

Explore uncertainty quantification for kinetic equations with random inputs in this comprehensive lecture. Delve into recent advancements in the field, addressing challenges posed by uncertainties in microscopic interaction details, boundary conditions, and initial data. Examine efficient numerical methods developed to combat the curse of dimensionality, including Monte Carlo methods, multi-fidelity approaches, and stochastic Galerkin particle methods. Cover key topics such as PDEs with random inputs, quantities of interest, computational aspects of UQ for PDEs, and various techniques like Monte Carlo sampling and Stochastic Galerkin methods. Investigate the application of uncertainty quantification to kinetic equations and their hydrodynamic limits, supported by a thorough literature survey.

Intro
Outline of the course
Motivations
Uncertainty quantification (UD)
PDEs with random inputs
Quantities of interest
Computational aspects of UQ for PDES
Overview of techniques
Some general references
Monte Carlo (MC) sampling methods
Stochastic Galerkin (SG) methods
Uncertainty in kinetic equations
Hydrodynamic limits