We here present a collection of benchmark problems for ordinary differential equation (ODE) system identification from time series data. We consider problems where both structure (the form of the ODEs) and parameters are unknown. The problems are all related to biological applications and consist of a combination of problems that have been collected and translated from the biological literature, as well as a number of newly designed problems. However, the way problems are defined is not application specific and can be used in many areas.
The identification problems are defined mathematically as optimization problems, and are represented in a file format designed for this purpose. The format makes it easy to define and exchange identification problems, and a problem is fully defined in a single file. Please note that since these problems are optimization problems and not models, it is not possible to represent such problems in SBML. See the Introduction for more information.
The purpose of the collection is to facilitate evaluation of identification algorithms during development, and to enable comparisons between different algorithms. We provide not just the problems, but also the best known solution of every problem, as well as any known source model. We also provide the possibility to solve identification problems online by running on our server.
Detailed documentation and supplementary software is available in the Documentation. The official publication presenting the collection is Gennemark and Wedelin, Benchmarks for identification of ordinary differential equations from time series data, Bioinformatics 25(6):780-6. More problems have subsequently been added to the collection, see the documentation.
Please contact Peter Gennemark and Dag Wedelin if you wish to submit a problem to the collection, or if you have found a better solution to an existing problem! We are also interested in feedback on how to best define and represent identification problems.