**Participants:**
O. Le Maître,
D. Lucor[1] and
L. Mathelin,

Real physical systems are generally incompletely characterized or subjected to irreducible variability, which makes their numerical modeling uncertain. Examples of uncertainty sources include the geometry, the external forcing and the physical properties of system. As simulation tools are improving, both in terms of accuracy and complexity, it becomes more and more important to account for these uncertainties in order to fairly assess the validity of model-based numerical predictions, performing for instance global sensitivity analyses to hierarchize the importance of different sources of uncertainty. Uncertainty Quantification methods have been developed at LIMSI over the last decade, relying on stochastic (probabilistic) approaches where uncertainty sources are treated as random input of the numerical model.

To predict and analyze the variability in the model solution induced by uncertainty sources (the so-called uncertainty propagation task), Polynomial Chaos expansions and general Stochastic Spectral methods have been implemented and are routinely used in complex models, either through Stochastic Galerkin projection or non-intrusive (black-box) approaches. These methodologies have been continuously improved to tackle challenging problems in the most efficient and computationally affordable way. In particular, researches at LIMSI have pioneered several advanced techniques such as stochastic multi-wavelets and multi-resolution schemes for discontinuous problems, low-rank (PGD) and sparse tensor representations, sparse grid methods, and the preconditioning of non-intrusive methods. More recently, researches have also considered various extensions of stochastic Spectral methods for Bayesian inference, stochastic inverse problems and data assimilation, as well as applications to stochastic simulators modeling systems driven by noise or having inherent random dynamics.

Researches performed at LIMSI have been applied to various types of mathematical models (elliptic, parabolic, hyperbolic, ordinary differential equations) as demanded by the physical applications. These applications have mostly concerned fluid flows: incompressible and compressible Navier-Stokes equations, turbulent flows, natural convection, shallow water flows, Darcy and porous media flows and aero-elasticity problems. Recent applications have concerned hemodynamics and artery flows, ocean dynamic simulations, wildfire propagation, bioengineering, and reactive systems.

**Main collaborations:**

MIT (Y. Marzouk), Duke University (W. Atquino), SRI-UQ center at KAUST (O. Knio and R. Tempone), Brown University (G. Karniadakis), SANDIA (H. Najm and B. Debusschere), USC (R. Ghanem), GeM-Centrale Nantes, MSME-UPE, Cermics-Ecole des Ponts, Dept. Math-UVSQ, LJLL-UPMC, ENSAM, ONERA, CERFACS, LIF-UPMC.

**Industrial partnerships:**

CEA (DEN, DAM), ONERA, ANDRA

See also: UQ activity at LIMSI and UQ publications at LIMSI