Stochastic Partial Differential Equations

Stochastic Partial Differential Equations (SPDEs)

Details

 

Mathematical models are widely used in physics and engineering applications as predictive tools. However, in many situations, the input parameters of the model are uncertain due to either a lack of knowledge or an intrinsic variability of the system. Examples are the study of subsurface phenomena, biological tissues, complex materials, whose properties are often heterogeneous, not perfectly characterized and, possibly, changing in time in an uncertain way.

In this line of research we consider the case in which the uncertainty can be described reasonably well in a probabilistic setting and we focus on the problem of effectively propagating it from the input parameters to the output quantities of interest of the mathematical model. In particular we focus on non-intrusive numerical methods that imply solving the problem for a well chosen set of input parameters and make inference on the statistical properties of the output quantities based on the corresponding evaluations.
 
 
 

Collaborators

  • Raul Tempone (KAUST)
  • Mohammad Motamed (KAUST)
  • Fabio Nobile (EPFL & Politecnico di Milano)
  • Ivo Babuska (UT Austin, TX)
  • Lorenzo Tamellini (Politecnico di Milano)
  • Giovani Migliorati (Politecnico di Milano)
  • Joakim Beck (UCL, London, UK)


Publications