A Posteriori Error Estimates for the Solution of Variational Inverse Problems

Abstract

Dynamically data-driven application systems integrate computational simulations and physical measurements in a symbiotic feedback control system. Inverse problems in this framework use data from measurements along with a numerical model to estimate the parameters or state of a physical system of interest. Uncertainties in both the measurements and the computational model lead to inaccurate estimates. This work develops a methodology to estimate the impact of different errors on the variational solutions of inverse problems. The focus is on time evolving systems described by differential equations, and on a particular class of inverse problems, namely, data assimilation. The computational algorithm uses first order and second order adjoint models. In a deterministic setting the methodology provides a posteriori error estimates for the inverse solution. In a probabilistic setting it provides an a posteriori quantification of uncertainty in the inverse solution, given the uncertainties in the model and data....