Approximation errors in nonstationary inverse problems

Abstract

Inverse problems are known to be very intolerant to both data errorsand errors in the forward model.With several inverse problems the adequately accurate forward model can turn out to becomputationally excessively complex.The Bayesian framework for inverse problems has recently been shown to enablethe adoption of highly approximate forward models.This approach is based on the modelling of the associated approximation errorsthat are incorporated in the construction of the computational model.In this paper we investigate the extension of the approximation error theory tononstationary inverse problems.We develop the basic framework for linear nonstationary inverse problemsthat allows one to use both highly reduced states and extended time steps.As an example we study the one dimensional heat equation.