  Neural networks have become a powerful tool as surrogate models to provide
numerical solutions for scientific problems with increased computational
efficiency. This efficiency can be advantageous for numerically challenging
problems where time to solution is important or when evaluation of many similar
analysis scenarios is required. One particular area of scientific interest is
the setting of inverse problems, where one knows the forward dynamics of a
system are described by a partial differential equation and the task is to
infer properties of the system given (potentially noisy) observations of these
dynamics. We consider the inverse problem of inferring the location of a wave
source on a square domain, given a noisy solution to the 2-D acoustic wave
equation. Under the assumption of Gaussian noise, a likelihood function for
source location can be formulated, which requires one forward simulation of the
system per evaluation. Using a standard neural network as a surrogate model
makes it computationally feasible to evaluate this likelihood several times,
and so Markov Chain Monte Carlo methods can be used to evaluate the posterior
distribution of the source location. We demonstrate that this method can
accurately infer source-locations from noisy data.
