Proceedings of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018 July 9–14, 2018. The role of the environment in front propagation Andrea Trucchia 1,2 and Gianni Pagnini 1,3 1 BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country – Spain 2 Department of Mathematics, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, E-48940 Leioa, Basque Country – Spain 3 Ikerbasque - Basque Foundation for Science, Calle de Mar´ ıa D´ ıaz de Haro 3, E-48013 Bilbao, Basque Country – Spain emails: atrucchia@bcamath.org, gpagnini@bcamath.org Abstract 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 Erd´ elyi–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. Key words: random front propagation – level set method – Erd´ elyi–Kober fractional diﬀusion – M-Wright/Mainardi function – Sensitivity Analysis MSC 2000: [2010] 35F21 – 60G22 – 60K37 – 65M08 – 49Q12 1 Introduction Front propagation plays an important role in many ﬁelds of applied science. It might happen that the propagating interface is embedded in a medium characterized by a random motion which implies some diﬀusion process. In classical diﬀusion, the process is Gaussian and the c CMMSE ISBN: 978-84-697-7861-6