A Benchmark for the Bayesian Inverse of Partial Differential Equations

A benchmark for the Bayesian inversion of coefficients in partial differential equations

We present a benchmark for the bayesian inversion of inverse problems that fills the gap between widely used simple test cases (such as superpositions of gaussians) and real applications that are difficult to replicate for developers of sampling algorithms.The benchmark is the determination of a spatially-variable coefficient, discretized by 64 values, in a poisson equation based on point measurements of the solution.We provide a complete description of the test case, and provide an open source implementation that can serve as the basis for further experiments.We have also computed samples, at a cost of some 30 years, of the posterior probability distribution from which we have generated detailed and accurate statistics against which other sampling algorithms can be tested.