Deep Gaussian Process Priors for Bayesian Inference in Nonlinear Inverse Problems

Understand

We study the use of a deep Gaussian process (DGP) prior in a general nonlinear inverse problem satisfying certain regularity conditions.

• We prove that when the data arises from a true parameter $\theta^*$ with a compositional structure, the posterior induced by the DGP prior concentrates around $\theta^*$ as the number of observations increases.
• The DGP prior accounts for the unknown compositional structure through the use of a hierarchical structure prior.
• As examples, we show that our results apply to Darcy's problem of recovering the scalar diffusivity from a steady-state heat equation and the problem of determining the attenuation potential in a steady-state Schr\"{o}dinger equation.