An Online Database of Benchmark Problems for Verification of Inverse Problems Computer Codes

Abstract

Verification and validation are a fundamental step in the development process of computer codes, particularly when seeking to numerically evaluate physical phenomena. Multiple methodologies can be applied, one of which is the use of benchmark solutions. The field of inverse problems is no exception, for not only the forward problem must be verified and validated, but also the inversion technique (such as minimization methods, Bayesian inference, and level-set methods). To address the latter, this work outlines an online database of benchmark inverse problems, for the purposes of verifying computer codes for inverse problems. This online database provides test problems with suggested values for the exact parameters and regularization parameters, as well as synthetic data and their respective estimated values. Both parameter and function estimation problems are available. This database will be continuously updated over time, with new problems and/or solutions via different techniques. Users are also free to contribute with problems/solutions of their own. This data being freely and easily accessible online will be of great value for young and upcoming researchers in the field of inverse problems. The database can be accessed at http://inversetoolkit.uff.br/.