Advances in Simulation-Based Uncertainty Quantification for Computational Solid and Structural Mechanics

Computational modeling of complex physical systems requires a rigorous accounting and quantification of uncertainties informed by available data. When data are abundant or probability laws can be justifiably assumed, this reduces to a conventional problem in uncertainty propagation where analysis is typically constrained by the computational cost of the model. When the model is expensive, advanced algorithms employing sparse sampling (random or deterministic) are necessary - often with the intension of constructing a computationally efficient surrogate model. In this talk, I discuss some recent advances in adaptive sampling for surrogate-based and Monte-Carlo based uncertainty quantification. These methods employ nonlinear projections of the high-dimensional solution onto a Grassmann manifold and use variations on the manifold to inform optimal sampling strategies. When data are scarce, model selection and statistical inference are coupled with the uncertainty propagation problem. In this case, I discuss methods in Bayesian model-selection and parameter estimation to quantify imprecise probabilities. These methods are then coupled with new importance sampling based approaches for propagation of uncertain probability distributions.