ISBN 9783843936965

978-3-8439-3696-5, Reihe Informatik

Fabian Franzelin
Data-Driven Uncertainty Quantification for Large-Scale Simulations

175 Seiten, Dissertation Universität Stuttgart (2017), Hardcover, B5

Zusammenfassung / Abstract

The computational demand of single large-scale simulation runs poses limits to the quantification of uncertainties (UQ), especially with non-intrusive methods that aim to approximate the response surface for the problem at hand. Numerical approximations suffer from the curse of dimensionality, the exponential dependency of the computational effort on the number of input parameters. To reduce the computational demand, an adaptive representation and exploration of such response surfaces is required. Furthermore, the uncertainty in the input affects heavily the uncertainty of the model's output, hence, reliable data-driven modeling of the input's uncertainty is essential. However, such inputs are rarely mutually independent, which decreases the efficiency of non-intrusive surrogates.

In this thesis, we propose to consider adaptive sparse grids to for data-driven uncertainty quantification for large-scale simulations. First, we introduce a new density estimation method based on extended sparse grids to describe the probability density of random input parameters. Furthermore, we provide algorithms to compute expectation values, covariances, marginal and conditional densities, which are required to define probabilistic transformations such as the Rosenblatt and the Nataf transformation. Second, we introduce different variants of sparse grids including new refinement criteria to propagate uncertainties for simulations that encounter non-smooth parameter dependencies or even shock phenomena. For smooth parameter dependencies we present Leja sequences as adaptive data-driven sampling scheme for arbitrary polynomial chaos expansion. Third, we combine the input modeling methods and the surrogate modeling techniques to solve inverse problems with Bayes' theorem.

We demonstrate the advantages of the newly introduced techniques on the basis of various engineering problems from crack propagation simulations in the context of material sciences to measuring leakage of carbon dioxide at a fault in a cap rock for subsurface flows.