An efficient Bayesian neural network surrogate algorithm for shape detection

Abstract

We present an efficient Bayesian algorithm for identifying the shape of an object from noisy far field data. The data is obtained by illuminating the object with one or more incident waves. Bayes' theorem provides a framework to find a posterior distribution of the parameters that determine the shape of the scatterer. We compute the distribution using the Markov Chain Monte Carlo (MCMC) method with a Gibbs sampler. The principal novelty of this work is to replace the forward far-field-ansatz wave model (in an unbounded region) in the MCMC sampling with a neural-network-based surrogate that is hundreds of times faster to evaluate. We demonstrate the accuracy and efficiency of our algorithm by constructing the distributions, medians and confidence intervals of non-convex shapes using a Gaussian random circle prior.