Scientific Computing Group Seminars - Detail View

Speaker: Y. Marzouk

Affiliation: Department of Aeronautics & Astronautics, MIT

Talk Title: Computationally Efficient Bayesian Inference Using Polynomial Chaos Expansions

Invited by: George Karniadakis

Time: Nov. 13 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

Predictive simulation of complex engineering systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data. Computationally intensive forward models, however, can render a Bayesian approach prohibitive. Polynomial chaos expansions, typically used in the forward propagation of uncertainty, are an extremely useful tool in the inverse context as well. We introduce a stochastic spectral formulation that accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior distribution. The posterior is constructed by either stochastic collocation or stochastic Galerkin methods. Theoretical convergence results are verified with several numerical examples---in particular, parameter estimation in transport equations and in chemical kinetic systems. We also extend this approach to the inference of spatially distributed quantities in a hierarchical Bayesian setting, achieving dimensionality reduction via Karhunen-Loeve representations of Gaussian process priors. Finally, we discuss the utility of polynomial chaos expansions in optimal experimental design---choosing experimental conditions to maximize information gain in parameters or outputs of interest. A Bayesian formulation of the design problem fully accounts for uncertainty in the parameters and relevant observables.