Interval-based Inverse Problems with Uncertainties

Abstract

Inverse problems in science and engineering aim at estimating model parameters of a physical system using observations of the model's response. Variational least square type approaches are typically adopted, solving the forward model, and then comparing the resulting modeled data with the actual measured data. The data mismatch is minimized and the process is iterated until the best match is achieved. However, data measurements are associated with uncertainties, and deterministic inverse algorithms hardly provide the associated error estimates for the model parameters. In this work, an interval-based iterative solution is presented to predict such errors, using adjoint-based optimization and the containment-stopping criterion.