Consistency of Variational Inference for Nonlinear Inverse Problems of Partial Differential Equations (opens in new tab)

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference transforms the inference problem into an optimization problem by introducing variational sets. Based on a modified ``prior mass and testing'' framework, we propose general conditions for three categories of inverse...