The dynamically growing field of uncertainty quantification and Bayesian identification is just beginning to enter into engineering practice. Stochastic analysis is not only used for simulating true randomness, but also to model our lack of knowledge of material properties, modeling errors or model coefficients. In the Bayesian framework, these inputs are handled as random variables, random fields or random processes.
The modern analysis of materials, buildings, infrastructures, machines, production processes, chemical reactions, and transportation is typically done by highly sophisticated nonlinear, often multi-scale models. Many of these models, however, are very sensitive to their input parameters or model coefficients, which are usually only known with limited precision. The coupling of probabilistic analysis with the governing equations enables the analysis of the propagation of these uncertainties through the model response. This approach provides not only methods to quantify uncertainties, analysis of robustness and global sensitivities, but also grounds a robust validation and parameter identification method in the framework of Bayesian inversion.
This planned summer course gives a theoretical background of how to tackle such problems and offer practical implementation techniques through a MATLAB library.
The main focus of the course is to simplify the computational burden of the sampling based methods, such as the Monte Carlo method and to rather use stochastic functional approximations of the uncertain parameters or uncertain fields and state variables. The approximation is done with the help of polynomials (general polynomial chaos expansion), or with other approximating functions such as radial basis functions or neural networks. With the help of this proxy modell the stochastic space is discretized. This discretized representation can be identified also with non-intrusive approaches and enables cheap evaluations of statistics, global sensitivities and sampling free approaches to probabilistic parameter identification. By increasing the number of parameters the used numerical approximation schemes often lead to extremely high dimensional problems, so that adaptive sparse representations and model reduction is of paramount importance to keep the whole problem computationally manageable.
Throughout the course and the workshop, after setting the theoretical and practical bases in a general framework, some more specific topics will be addressed, such as structural reliability, fragility assessment, handling parameter uncertainties in multi-scale modelling, and the involvement of machine learning and data mining techniques in engineering applications.
In the workshop a round table discussion and small presentations are meant to foster the interaction between researchers, practicing engineers, and students to exchange ideas, experiences and difficulties in an international and multidisciplinary scientific environment. Giving a talk on the workshop by attendees is not obligatory but strongly encouraged.
Dr. Noémi Friedman
Institute of Scientific Computing