SC²S Colloquium - August 19, 2015

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Date: August 19, 2015
Room: 02.07.023
Time: 3:00 pm, s.t.

Pablo Gómez: Adaptive Construction of Surrogate Models Based on Sparse Grid Interpolants for Bayesian Inverse Problems

In this paper we present an adaptive surrogate model based on sparse grid interpolation for a bayesian inverse Navier-Stokes problem. We introduce the concept of inverse problems from a bayesian perspective and a finite-difference method as forward model for the Navier-Stokes problem. The basic problem setup is a channel in which up to four obstacles are placed and velocity magnitude measurements are taken. From these measurements we want to infer the locations of the obstacles using a Metropolis-Hastings Markov chain Monte Carlo solver. Our surrogate model relies on a sparse grid interpolation of the forward model, which we then refine online by creating higher level sparse grids in areas of interest, i.e. likely obstacle locations. We present detailed results in the form of histograms for both the finite-difference method and our adaptive surrogate model. Overall we achieve a higher accuracy using a computationally less expensive model. Our approach is also applicable to other inverse problems which will be the feature of future research.