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Inference and experimental design in complex physical systems

Tuesday, February 8, 3:30PM
ACES 6.304

Youssef Marzouk

Predictive 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 complete foundation for inference and for the optimal selection of experiments and observations. Computationally intensive models, however, can render a Bayesian approach prohibitive.

Posterior simulation in Bayesian inference typically proceeds via Markov chain Monte Carlo (MCMC), but the associated computational expense and convergence issues are significant obstacles in large-scale problems. We introduce a new "map-based" inference methodology that entirely avoids Markov chain-based simulation, by constructing a map under which the posterior becomes the pushforward measure of the prior. Existence and uniqueness of a suitable map is established by casting our algorithm in the context of optimal transport theory. The proposed functions are computed using nonlinear optimization methods. We demonstrate the efficiency of the methodology by estimating spatially inhomogeneous transport properties in PDEs and rate parameters in chemical systems.

We also discuss computational approaches 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. Efficient evaluation of the objective function relies on polynomial surrogates constructed with adaptive and non-intrusive methods; stochastic optimization methods are then used to maximize expected utility. We demonstrate these methods on canonical experiments in combustion kinetics.

Host: R. Moser