In this work we study the role of a complex environment in the propagation of a front
with curvature-dependent speed. The motion of the front is split into a drifting part and
a fluctuating part. The drifting part is obtained by using the level set method, and the
fluctuating part by a probability density function that gives a comprehensive statistical
description of the complexity of the environment. In particular, the environment is
assumed to be a diffusive environment characterized by the Erdélyi–Kober fractional
diffusion. The evolution of the front is then analysed with a Polynomial Chaos surrogate
model in order to perform Sensitivity Analysis on the parameters characterizing the
diffusion and Uncertainty Quantification procedures on the modeled interface. Sparse
techniques for Polynomial Chaos allowed a limited size for the simulation databases.PhD Grant "La Caixa 2014
