A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models

Understand

We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensional parameter spaces.

• The contributions of this paper are two-fold; the first is the introduction of a neural network approach to approximating the solutions of Fredholm and Volterra integral equations of the first and second kind.
• The second is the development of a new, efficient deep learning-based method for Bayesian inversion applied to problems that can be described by PDEs or integral equations.
• To achieve this we introduce a surrogate model, and demonstrate how this allows efficient sampling from a Bayesian posterior distribution in which the likelihood depends on the solutions of PDEs or integral equations.