| Abstract: |
| In this talk we will discuss some recent results concerning the construction of efficient numerical methods for uncertainty quantification (UQ) in kinetic equations. In spite of the vast amount of existing research, both theoretically and numerically, the study of kinetic equations has mostly remained deterministic and ignored uncertainty. In reality, there are many sources of uncertainties that can arise in these equations as for instance incomplete knowledge of the interaction mechanism between particles/agents., imprecise measurements of the initial and boundary data, other sources of uncertainty like forcing and geometry, etc.
Understanding the impact of these uncertainties is critical to the simulations of the complex kinetic systems to validate the kinetic models, Recently we developed novel approaches to UQ of kinetic equations based on micro-macro Monte Carlo techniques which using control variate estimators based on the local equilibrium are capable to accelerate the slow statistical convergence of Monte Carlo methods. |
|