A Levenberg-Marquardt Algorithm for Sparse Identification of Dynamical Systems

Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this article, we introduce a flexible method for the sparse identification of dynamical systems described by ordinary differential equations. Our method relieves many of the requirements imposed by other methods that relate to the structure of the model and the dataset, such as fixed sampling rates, full state measurements, and linearity of the model. The Levenberg-Marquardt algorithm is used to solve the identification problem. We show that the Levenberg-Marquardt algorithm can be written in a form that enables parallel computing, which greatly diminishes the time required to solve the identification problem. An efficient backward elimination strategy is presented to construct a lean system model.

Automated summary

This article introduces a flexible method for the sparse identification of dynamical systems. The method alleviates the stringent requirements imposed by other methods, such as fixed sampling rates and full state measurements. The Levenberg-Marquardt algorithm is used to solve the identification problem, and a parallel computing form of the algorithm is presented to reduce the solving time. An efficient backward elimination strategy is also proposed to construct a lean system model.