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Model selection for dynamical systems via sparse regression and information criteria.

N M Mangan1,2, J N Kutz1, S L Brunton3

  • 1Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|September 8, 2017
PubMed
Summary
This summary is machine-generated.

We developed a new algorithm for selecting models of dynamical systems, even with many possibilities. This approach efficiently identifies the best model using information criteria, overcoming computational limits of standard methods.

Keywords:
data-driven discoveryinformation criteriamodel selectionnonlinear dynamicssparse regression

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Area of Science:

  • Dynamical Systems Modeling
  • Computational Science
  • Statistical Inference

Background:

  • Standard model selection methods struggle with a large number of candidate models due to computational intractability of information criteria.
  • Selecting the correct model for complex dynamical systems is crucial for accurate prediction and understanding.

Purpose of the Study:

  • To develop an efficient algorithm for model selection in dynamical systems, accommodating a combinatorially large number of candidate models.
  • To enable feasible computation of information criteria for a reduced set of candidate models, overcoming standard limitations.

Main Methods:

  • Utilized a sparse identification of nonlinear dynamics algorithm for initial sub-selection of candidate models.
  • Applied Pareto frontier optimization to identify a manageable subset of relevant models.
  • Computed Akaike information criteria (AIC) or Bayes information criteria scores for the refined model set.

Main Results:

  • The algorithm successfully reduced the computational burden of model selection for complex dynamical systems.
  • AIC scores effectively categorized candidate models into 'strong support,' 'weak support,' and 'no support' groups.
  • The method accurately recovered canonical dynamical systems, including SEIR, Burgers' equation, and Lorenz equations, identifying the correct model with strong support.

Conclusions:

  • The proposed algorithm provides an automatic and principled approach for selecting the most informative model from a vast set of candidates.
  • This method enhances the feasibility and accuracy of model selection for time-series data in dynamical systems.
  • The approach demonstrates robust performance across various complex dynamical systems.