Benchmarks for identification of ordinary differential equations from time series data

Motivation: In recent years, the biological literature has seen a significant increase of reported methods for identifying both structure and parameters of ordinary differential equations (ODEs) from time series data. A natural way to evaluate the performance of such methods is to try them on a sufficient number of realistic test cases. However, weak practices in specifying identification problems and lack of commonly accepted benchmark problems makes it difficult to evaluate and compare different methods. Results: To enable better evaluation and comparisons between different methods, we propose how to specify identification problems as optimization problems with a model space of allowed reactions (e.g. reaction kinetics like Michaelis - Menten or S-systems), ranges for the parameters, time series data and an error function. We also define a file format for such problems. We then present a collection of more than 40 benchmark problems for ODE model identification of cellular systems. The collection includes realistic problems of different levels of difficulty w.r.t. size and quality of data. We consider both problems with simulated data from known systems, and problems with real data. Finally, we present results based on our identification algorithm for all benchmark problems. In comparison with publications on which we have based some of the benchmark problems, our approach allows all problems to be solved without the use of supercomputing