Title: Uncertainty quantification and Bayesian inference for fractional diffusion models
Author: Olivier Le Maître (Ecole Polytechnique)

Fractional diffusion and Fokker-Planck equations are attractive alternatives for modeling anomalous diffusion and dispersion processes in complex media (e.g., the passive transport by fluid flows in porous media or turbulent flows). The analysis of deterministic fractional models is still the subject of intensive works, and efficient numerical schemes are still under development. One crucial aspect of fractional models that remains primarily untouched concerns the sensitivity with the model parameters of the fractional solution. Similarly, identifying the fractional coefficients from experimental observations has not been extensively analyzed.

This presentation will discuss some of our recent works on a) the development of a UQ method for the time-fractional diffusion model and b) the joint identification of fractional and diffusion coefficients in spatial fractional diffusion problems. Specifically, we will detail a stochastic spectral approach that relies on Galerkin projections for the time-fractional problem. Concerning identifying model parameters, we will discuss a Bayesian framework and the information gained from types of measurements on the spatial fractional diffusion solution. Finally, we will discuss the challenges extending of these techniques to applications involving large-scale models.