Stochastic Partial Differential Equations (SPDEs)
SPDEs are partial differential equations with random terms which are due to uncertainty in the models. They arise in many multidimensional physical problems. Examples for the source of uncertainty include the variability of soil permeability in subsurface aquifers and heterogeneity of materials with microstructure. We work on the analysis and computation of elliptic, parabolic and hyperbolic equations with random data.
Overview
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 inferences 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)
Related People
Related Researchers
Mohammad Motamed
- Postdoctoral Research Fellow, Stochastic Numerics Research Group
Joakim Beck
- Research Scientist, Stochastic Numerics Research Group