Machine learning methods have revolutionized studies in several areas of knowledge, helping to understand and extract information from experimental data. Recently, these data-driven methods have also been used to discover structures of mathematical models. The sparse identification of nonlinear dynamics (SINDy) method has been proposed with the aim of identifying nonlinear dynamical systems, assuming that the equations have only a few important terms that govern the dynamics. By defining a library of possible terms, the SINDy approach solves a sparse regression problem by eliminating terms whose coefficients are smaller than a threshold. However, the choice of this threshold is decisive for the correct identification of the model structure. In this work, we build on the SINDy method by integrating it with a global sensitivity analysis (SA) technique that allows to hierarchize terms according to their importance in relation to the desired quantity of interest, thus circumventing the need to define the SINDy threshold. The proposed SINDy-SA framework also includes the formulation of different experimental settings, recalibration of each identified model, and the use of model selection techniques to select the best and most parsimonious model. We investigate the use of the proposed SINDy-SA framework in a variety of applications. We also compare the results against the original SINDy method. The results demonstrate that the SINDy-SA framework is a promising methodology to accurately identify interpretable data-driven models.
Supplementary information: The online version contains supplementary material available at 10.1007/s11071-022-07755-2.
Keywords: Data-driven methods; Differential equations; Model selection; Sensitivity analysis; Sparse identification.
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