Project Details
Projekt
Efficient Bayesian Multi-fidelity Schemes for Analysis and Design of Complex Multiphysics Systems
Subject Area
Applied Mechanics, Statics and Dynamics
Mechanics
Mechanics
Term
from 2017 to 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 347224436
The consideration of multiple physical fields is of paramount importance in the design process of engineering systems. Computational tools for analysis, design, and optimization of structures have evolved to account for these effects and enable the study of such complex systems. Nevertheless, a purely deterministic analysis can lead to unsatisfactory and unreliable results if any component of the models employed cannot be precisely determined or exhibits random variability. Such epistemic and aleatoric uncertainties are encountered in the overwhelming majority of real-world systems. The predictive capabilities of computational models, as well as the resilience of the systems designed, can be significantly improved if a probabilistic point of view is adopted and the uncertainties in the input parameters are accounted for in the model. Although many strategies for uncertainty quantification (UQ) have been proposed in recent years, current approaches exhibit poor scalability with the stochastic dimension and require an exuberant number of evaluations of the expensive, nonlinear forward model.The challenge we propose to undertake in this project is the development of a novel and efficient UQ framework that can be used for analysis and design of complex, nonlinear, multiphysics models with high stochastic dimension. Applications will involve strongly coupled problems such as fluid-structure-interaction. The proposed set of UQ methods will be able to handle complex, real-world systems, characterized by high-dimensional parametric uncertainties. The methods developed will provide certifiable estimates for the statistics of the output quantities of interest, as well as sensitivity measures for the uncertain model input parameters. The hitherto prohibitive computational costs associated with UQ in such complex and challenging settings will be mitigated by rigorously incorporating information from inexpensive, lower-fidelity models. These are combined with a few, intelligently selected evaluations of the expensive, high-fidelity model, in order to obtain accurate estimates at a fraction of the cost compared to current UQ methods. Moreover, by adopting a Bayesian approach, credible intervals can be computed which quantify the confidence in the estimates as well as guide adaptive refinements. In addition, the UQ approach will also serve as the basis for the development of a novel stochastic optimization framework for the design of complex systems in the presence of uncertainties. The proposed methods are very general and will be applicable to a wide range of problems. As example, large-scale, nonlinear problems arising in cardiovascular biomechanics will be used to demonstrate capabilities and efficiency of the methods.The proposal directly addresses several of the most fundamental questions posed by the priority program. A set of benchmark problems will be developed that will enable comparison as well as cross-pollination of different perspectives.
DFG Programme
Priority Programmes
