The increasing demand for quality and reliability in scientific computing makes the quantification of uncertainties in mathematical models and input data a crucial task. Including Uncertainty Quantification in scientific computing leads to a paradigm shift from purely deterministic problems to the stochastic models. In addition, the development of new hardware technologies allows us to address the challenges of uncertainty quantification associated with the increasing complexity of numerical computations, which requires the adaptation and new development of exascale computing methods.

The overall scientific goal of bridging the gap between uncertainty quantification and high performance computing is therefore addressed by several interacting research tasks at EMCL:

•  Non-intrusive and intrusive uncertainty quantification for systems of partial differential equations (PDEs) and ordinary differential equations (ODEs) with uncertain parameters;
• Model reduction techniques to overcome the curse of dimensionality and to improve parallelism;
• Efficient accelerator and preconditioning technologies for use on large-scale supercomputer clusters;
• Open source software development to make the implementations available to the global research community;
• Real-world applications, with a strong focus on complex geometries and coupled systems.