Abstract:
This talk addresses the topic of uncertainty quantification in high-dimensional model-based Bayesian inverse problems with an application to linear elastostatic problems. For that purpose, a probabilistic mechanical model is proposed, recasting the traditional forward problem formulation to an inference task. The approach falls into the category of intrusive methods, where, in contrast to non-intrusive approaches that use black-box models, incomplete information and sources of randomness can be modeled directly at their point of origin. Variational approximations are introduced and a computational strategy developed. The framework enables a flexible modeling approach, both in terms of the physical model and the variational approximation. Its feasibility is demonstrated by solving three problem scenarios in the context of linear elastostatics: (1) classical well-posed forward problems, (2) inverse problems with the goal of material parameter identification and (3) inverse problems including the estimation of constitutive model error.