# hpfem/esco2012-boa

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 \title{Bayesian Parameter Identification for Nonlinear Systems} \tocauthor{B. Rosic} \author{} \institute{} \maketitle \begin{center} {\large \underline{Bojana Rosic}}\\ TU Braunschweig\\ {\tt bojana.rosic@tu-bs.de} \\ \vspace{4mm}{\large Oliver Pajonk}\\ SPT Group GmbH Hamburg\\ {\tt o.pajonk@tu-bs.de} \\ \vspace{4mm}{\large Anna Kucerova}\\ TU Prague\\ {\tt anicka@cml.fsv.cvut.cz} \\ \vspace{4mm}{\large Jan Sykora}\\ TU Prague\\ {\tt jan.sykora.1@fsv.cvut.cz} \\ \vspace{4mm}{\large Hermann G. Matthies}\\ TU Braunschweig\\ {\tt wire@tu-bs.de} \end{center} \section*{Abstract} Inverse problems are important in engineering science and appear very frequently such as for example in estimation of material porosity and properties describing irreversible behaviour, control of high-speed machining processes etc. At present, most of identification procedures have to cope with ill-possedness as the problems are often considered in a deterministic framework. However, if the parameters are modelled as random variables the process of obtaining more information through experiments in a Bayesian setting becomes well-posed \cite{Tarantola}. In this manner the Bayesian information update can be seen as a minimisation of variance. In this work we use the functional approximation of uncertainty and develop a purely deterministic procedure for the updating process \cite{Rosic,Pajonk}. This is then contrasted to a fully Bayesian update based on Markov chain Monte Carlo \cite{Gamerman} sampling on a few numerical nonlinear examples based on plasticity and nonlinear diffusion models. \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{Tarantola} {\sc A. Tarantola}. { Inverse Problem Theory and Methods for Model Parameter Estimation}. Society for Industrial and Applied Mathematics, Philadelphia, 2005. \bibitem{Pajonk} {\sc O. Pajonk and B. Rosic and A. Litvinenko and H. G. Matthies}. {A Deterministic Filter for Non-Gaussian Bayesian Estimation}. Informatikbericht 2011-04, TU Braunschweig, 2011.. \bibitem{Rosic} {\sc B. Rosic and A. Litvinenko and O.Pajonk undefined and H. G. Matthies}. {Direct Bayesian Update of Polynomial Chaos Representations}. Informatikbericht 2011-02, TU Braunschweig, 2011.. \bibitem{Gamerman} {\sc D. Gamerman and H. F. Lopes}. {Markov Chain Monte Carlo: stochastic simulation for Bayesian inference}. Chapman and Hall, Florida. \end{thebibliography}