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Uncertainty and Bayesian inference in inverse problems

Speaker: Dr. Youssef Marzouk, Massachusetts Institute of Technology"Uncertainty and Bayesian inference in inverse problems"Predictive simulation rests on validated models, which often must be conditioned on indirect observations. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the objects of inference. Inverse problemsâ€"representing indirect estimation of model parameters, inputs, or structural componentsâ€"can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high dimensionality, as when the unknown is a spatial field.We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also pursue dimensionality reduction for the inference of spatiotemporal fields, using truncated Karhunen-Loève representations of Gaussian process priors. These approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous transport properties.

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes