Model selection for dynamical systems via sparse regression and information criteria

N. M. Mangan*, J. N. Kutz, S. L. Brunton, J. L. Proctor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

169 Scopus citations

Abstract

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number of candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows feasible computation of Akaike information criteria (AIC) or Bayes information criteria scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time-series data. Specifically, we show that AIC scores place each candidate model in the strong support, weak support or no support category. The method correctly recovers several canonical dynamical systems, including a susceptible-exposedinfectious-recovered disease model, Burgers' equation and the Lorenz equations, identifying the correct dynamical system as the only candidate model with strong support.

Original languageEnglish (US)
Article number20170009
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2204
DOIs
StatePublished - Aug 1 2017

Keywords

  • Data-driven discovery
  • Information criteria
  • Model selection
  • Nonlinear dynamics
  • Sparse regression

ASJC Scopus subject areas

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics

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