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AMCS Seminar: Sparse-grids-based Uncertainty Quantification of geochemical compaction of sedimentary basins

Start Date: September 18, 2018
End Date: September 18, 2018

By Dr. Lorenzo Tamellini (CNR-IMATI Pavia, Italy)
 
In this work we propose a methodology based on sparse grids for the Uncertainty Quantification (UQ) of sedimentary basins undergoing mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. We discuss both forward and inverse UQ for this problem, whose quantities of interest (QoI) are the in-depth profiles of porosity, temperature and pressure at T=today. The methodology proposed is based on a sparse-grid approximation of the QoI, and in particular we will discuss an efficient methodology for the computation of the Sobol indices, to evaluate the impact of each random parameter on the total variability of the QoI. The inverse problem will be tackled with a Maximum Likelihood approach, sped up by replacing the full model evaluation with its sparse-grid approximate counterpart. We then consider the case of multi-layered basins, in which each layer is characterized by a different material. The multi-layered structure gives rise to discontinuities in the map from the uncertain parameters to the QoI. Because of these discontinuites, an appropriate treatment is needed to apply sparse grids quadrature and interpolation for UQ purposes. To this end, we propose a two-steps methodology which relies on a change of coordinates to align the interfaces among layers of different materials; note that the map from the physical to the reference domain is random because the location of the interfaces also depends on the values of the random parameters. Once this alignement has been computed (again by means of a sparse grid), a standard sparse-grid-based UQ analysis of the QoI can be performed within each layer. This procedure can then be seen as a composition of sparse grids, or ``deep sparse grid approximation''. The effectiveness of this procedure is due to the fact that the physical locations of the interfaces among layers feature a smooth dependence on the random parameters and are therefore themselves amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through some synthetic test cases.
 
Biography: I am currently a researcher at CNR-IMATI Pavia. Previously, I was a postdoc at the Department of Mathematics of Pavia University with prof. Giancarlo Sangalli, and at EPFL (Lausanne) with prof. Fabio Nobile (MATHICSE-CSQI group). Fabio Nobile was also my PhD advisor at Politecnico di Milano (MOX lab, Department of Mathematics). My main scientific interests are Uncertainty Quantification, Isogeometric Analysis, and mathematical aspects of 3D printing.

More Information:

For more info contact: Professor Raul Tempone: email: raul.tempone@kaust.edu.sa
 
Date: Tuesday 18th Sep 2018
Time:10:00 AM - 11:00 AM
Location: Building 1, Level 4, Room 4214
Refreshments: will be available at 9:45am.