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COMPUTE seminars


1 December at 11.00 in Lundmarksalen, coffee/tea from 10.30

Bojana Rosić (TU Braunschweig): Uncertainty quantification in a Bayesian setting

Concrete and human bone tissue are typical examples of materials which exhibit randomness in the mechanical response due to an uncertain heterogeneous micro-structure. In order to develop an appropriate probabilistic macro-scale mathematical description, the essential step is to address the material as well as possible other sources of uncertainties (e.g. excitations, change in geometry , etc.) in the model. By extending already existing deterministic models derived from Helmholtz free energy and the dissipation functions characterising ductile or quasi-brittle behaviour, the goal of this talk is to identify and quantify uncertainty in the system response. For this purpose a Bayesian probabilistic setting is considered in which the modeller's a priori knowledge about the model parameters and the available set of data obtained by experiments are taken into account when identifying the corresponding probability distribution functions of unknown parameters. Identification in the form of Bayesian inverse problems - in particular when experiments are performed repeatedly - requires an effcient solution and representation of possibly high dimensional probabilistic forward problems, i.e. the estimation of the measurement prediction given prior assumption. An emergent idea is to propagate parameter uncertainties through the model in a Galerkin manner in which the solution of the corresponding differential equations is represented by a set of stochastic basis polynomials, the cardinality of which grows exponentially. To allow an effcient solution of high-dimensional problems this talk will present the new low-rank Galerkin schemes combined with Bayesian machine learning approaches.

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This page was last modified on 30 November 2017.