Topic

Uncertainty Quantification for Partial Differential Equations (UQ4PDE): Numerical Analysis and Scientific Computing

The numerical treatment of Partial Differential Equations (PDEs) with uncertain input and/ or solutions has undergone dramatic development during the past years, in particular in connection with efficient numerical methods for computational uncertainty quantification.

A core theme are efficient numerical methods for direct and inverse problems for PDEs with uncertain, distributed input.
Uncertainty parametrization renders uncertain distributed inputs parametric deterministic, and the mathematical and computational
issue is efficient approximation and computation of PDEs on high-dimensional parameter spaces.

The efficient computational treatment of many-parametric, deterministic PDEs is at the core of computational UQ, and of the ZSS2018.

Specific (mathematical and computational) themes of ZSS2018:

- Multilevel Monte Carlo
- high-dimensional numerical approximation and integration
- generalized polynomial chaos (gpc)
- multilevel discretizations in UQ (multigrid, wavelets, FEM, BEM, FVM)
- multimodel discretizations in UQ
- Parametric regularity for PDEs
- Stochastic Galerkin/ Collocation/ Least Squares / Compressed Sensing
- PDE approximations and their mathematical foundations
- Representation and matrix/tensor formatted compression of two- and
  k-point correlation functions of random fields
- Numerical Approximation of Statistical solutions and correlation
  measures for nonlinear PDEs.

Organizers:
H. Ammari, R. Hiptmair, S. Mishra, Ch. Schwab (ETH)
R. Abgrall, S. Sauter (University of Zurich)