Youssef Marzouk
MIT, Department of Aeronautics and Astronautics

Title:

"Algorithms for inference and experimental design in complex physical systems"
 
Abstract:

Simulation of complex physical 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 and for the optimal selection of experiments and observations. Computationally intensive models, however, can render a Bayesian approach prohibitive.

We will show that stochastic spectral methods, which have seen extensive development in the context of "forward" uncertainty propagation, are a useful tool for inference as well. We introduce a stochastic spectral formulation that accelerates Bayesian inference via rapid exploration of a surrogate posterior distribution. Theoretical convergence results are verified with several numerical examples---in particular, parameter estimation in transport processes and in chemical kinetic systems. We also extend this approach to high-dimensional and ill-posed inverse problems, estimating distributed quantities in a hierarchical Bayesian setting.

We will also discuss computational strategies for optimal experimental design---choosing experimental conditions to maximize information gain in parameters or outputs of interest. We propose a general Bayesian framework for experimental design with nonlinear simulation-based models, accounting for uncertainty in model parameters, experimental conditions, and observables. We then discuss efficient evaluation of the associated objective functions, coupled with stochastic optimization methods to maximize expected utility.

ymarz@mit.edu

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