The mini deals with state of the art reduced order methods for uncertainty quantification in parametric computational fluid dynamics (CFD) problems dealing with data assimilation, data reconstruction, random inputs. Special attention is devoted to inverse problems for optimisation and control, as well as to nonlinear problems. Complex applications of the methodology are considered in industrial setting, as well as in medicine.
08:30
- NEW - Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics
Saddam N Y Hijazi | SISSA Trieste | Italy
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Authors:
Saddam N Y Hijazi | SISSA Trieste | Italy
Giovanni Stabile | SISSA Trieste | Italy
Andrea Mola | SISSA Trieste | Italy
Gianluigi Rozza | SISSA Trieste | Italy
This work presents the implementation of Uncertainty Quantification (UQ) methods for CFD problems based on non-intrusive Polynomial Chaos Expansion (PCE) exploiting both full order and reduced order solvers. The Reduced Order Model is based on a POD-Galerkin approach. A non-intrusive PCE approach is first applied directly to the Full Order Model (FOM) solutions. Later the same methodology is implemented using reduced-order model solutions. Finally, we test the reliability of the POD-Galerkin surrogate model as an input to the non-intrusive PCE.
09:00
Model order reduction for UQ in turbulent CFD
Giovanni Stabile | SISSA | Italy
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Giovanni Stabile | SISSA | Italy
Gianluigi Rozza | SISSA, Int. School for Advanced Studies, Trieste | Italy
We analyse the state of the art for reduced order methods with a data driven approach for uncertainty quantification problems in CFD with turbulent flows. Classic benchmark test cases are studied. Application perspectives are provided.
09:30
Neural Networks as Control Variates for UQ in Ice Sheet Flow
Bassel Saleh | Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin | United States
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Bassel Saleh | Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin | United States
Omar Ghattas | Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin | United States
Thomas O'Leary Roseberry | Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin | United States
Umberto Villa | Washington University in St. Louis | United States
One application of multifidelity modeling in uncertainty quantification is to use a low-fidelity surrogate as a control variate, a technique in which one exploits the statistical correlation between the outputs of high- and low-fidelity models to reduce the variance of the estimated statistics of a quantity of interest. One candidate for a low-fidelity model of interest in many applications is an artificial neural network, trained on data generated through evaluations of the high-fidelity model. A major challenge with this approach in large-scale physical settings is the fact that high-dimensional inputs require large network architectures that become computationally intractable to train and employ cheaply. We propose a methodology for reducing the dimension of the model parameter in a PDE problem by exploiting curvature information in the parameter-to-observable map to identify informative directions in parameter space. The result is a low-dimensional representation of the parameter that can be used as input to a much smaller feedforward neural network than otherwise possible. We then demonstrate that a network constructed this way can be a viable control variate. We test our methods by doing forward UQ on a model for Antarctic ice sheet flow. We also compare our results with other classes of low-fidelity models used as control variates, such as traditional reduced order models and Taylor approximations.
10:00
Weighted model order reduction techniques for advection dominated problems with selective stabilization
Davide Torlo | University of Zurich | Switzerland
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Authors:
Davide Torlo | University of Zurich | Switzerland
Francesco Ballarin | SISSA | Italy
Gianluigi Rozza | SISSA, Int. School for Advanced Studies, Trieste | Italy
Model order reduction (MOR) techniques are particularly useful and important when we deal with parametric problems, in particular in many-query and Monte Carlo frameworks, where many solutions for different parameters are required. In order to use MOR algorithms on stochastic problems, weighted modifications of the classical POD and greedy algorithm have been proposed. Here, the minimized error is considered with respect to the probability distribution of the parameter domain.
We draw our attention on advection--diffusion problems, in the advection dominated regime. These problems require stabilization terms in the classical finite element formulation. In the MOR context, we see that the stabilization can be applied in the Offline and/or in the Online phase. According to the chosen stabilization we have different errors and different computational costs. To compute some statistical quantities of the stochastic PDEs, we propose a selective stabilization in the Online phase, which does not affect significantly the global error, but it leads to computational advantages in the Online phase of the process.