We present our recent efforts towards uncertainty quantification for large-scale computational mechanics. The talk has three parts.
In the first part, we present a reduce-then-sample approach to efficiently study the probabilistic response of turbomachinery flow due to random geometric variation of bladed disk. We first propose a model-constrained adaptive sampling approach that explores the physics of the problem under consideration to build reduced-order models. Monte Carlo simulation is then performed using the cost-effective reduced model. We demonstrate the effectiveness of our approach in predicting the work per cycle with quantifiable uncertainty.
In the second part of the talk, we consider the shape inverse problem of electromagnetic scattering. We address this large-scale inverse problems in a Bayesian inference framework. Since exploring the Bayesian posterior is intractable for high dimensional parameter space and/or expensive computational model, we propose a Hessian-informed adaptive Gaussian process response surface to approximate the posterior. The Monte Carlo simulation task, which is impossible using the original posterior, is then carried out on the approximate posterior to predict the shape and its associated uncertainty with negligible cost.
In the last part of the talk, we address the problem of solving globally large-scale seismic inversion governed by the linear elasticity equation. We discuss a mesh-independent uncertainty quantification method for full wave form seismic inversion exploiting the compactness of the misfit Hessian and low rank approximation.