Model selection for dynamical systems via sparse regression and information criteria

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 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 for a tractable computation of AIC (Akaike information criteria) or BIC (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 {\em strong support}, {\em weak support} or {\em no support} category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptible-exposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support.