A Levenberg-Marquardt algorithm for sparse identification of dynamical systems

TL;DR

This paper presents a flexible Levenberg-Marquardt based method for sparse identification of dynamical systems that overcomes many limitations of existing methods, enabling faster and more practical model discovery from data.

Contribution

It introduces a novel Levenberg-Marquardt algorithm formulation for sparse system identification that is adaptable to various data conditions and supports parallel computation.

Findings

Enables sparse identification without fixed sampling or full state measurements

Reduces computation time through parallelizable Levenberg-Marquardt implementation

Provides an efficient backward elimination strategy for lean model construction

Abstract

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 paper, 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 data set, 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.