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SINDy-SA framework: enhancing nonlinear system identification with sensitivity analysis.

Gustavo T Naozuka1, Heber L Rocha2, Renato S Silva1

  • 1Laboratório Nacional de Computação Científica, Petrópolis, RJ Brazil.

Nonlinear Dynamics
|September 5, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new data-driven modeling approach, integrating sparse identification of nonlinear dynamics (SINDy) with global sensitivity analysis (SA). This SINDy-SA framework accurately identifies interpretable mathematical models by prioritizing important terms, improving upon existing methods.

Keywords:
Data-driven methodsDifferential equationsModel selectionSensitivity analysisSparse identification

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Area of Science:

  • * Computational Science and Engineering
  • * Data-driven Modeling
  • * Applied Mathematics

Background:

  • * Machine learning methods are increasingly used for extracting information from experimental data.
  • * Discovering mathematical model structures from data is a key challenge.
  • * The sparse identification of nonlinear dynamics (SINDy) method identifies nonlinear dynamical systems but relies on a crucial threshold parameter.

Purpose of the Study:

  • * To develop an improved data-driven method for identifying nonlinear dynamical systems.
  • * To overcome the limitations of the SINDy threshold parameter.
  • * To create a robust framework for accurate and interpretable model discovery.

Main Methods:

  • * Integration of the sparse identification of nonlinear dynamics (SINDy) method with global sensitivity analysis (SA).
  • * Hierarchization of model terms based on their importance to the quantity of interest.
  • * Formulation of experimental settings, model recalibration, and model selection techniques.

Main Results:

  • * The proposed SINDy-SA framework effectively identifies interpretable data-driven models.
  • * Sensitivity analysis circumvents the need for an arbitrary SINDy threshold.
  • * The framework demonstrates accuracy and robustness across various applications.

Conclusions:

  • * The SINDy-SA framework offers a promising advancement in data-driven model identification.
  • * This approach enhances the interpretability and accuracy of discovered mathematical models.
  • * The methodology provides a more reliable alternative to the original SINDy method.