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The performance of estimated models is often evaluated in terms of theirpredictive capability. In this study, we investigate another important aspectof estimated model evaluation: the disparity between the statistical anddynamical properties of estimated models and their source system. Specifically,we focus on estimated models obtained via the regression method, sparseidentification of nonlinear dynamics (SINDy), one of the promising algorithmsfor determining equations of motion from time series of dynamical systems. Wechose our data source dynamical system to be a higher-dimensional instance ofthe Lorenz 2005 type II model, an important meteorological toy model. Weexamine how the dynamical and statistical properties of the estimated modelsare affected by the standard deviation of white Gaussian noise added to thenumerical data on which the estimated models were fitted. Our results show thatthe dynamical properties of the estimated models match those of the sourcesystem reasonably well within a range of data-added noise levels, where theestimated models do not generate divergent (unbounded) trajectories.Additionally, we find that the dynamics of the estimated models becomeincreasingly less chaotic as the data-added noise level increases. We alsoperform a variance analysis of the (SINDy) estimated model's free parameters,revealing strong correlations between parameters belonging to the samecomponent of the estimated model's ordinary differential equation.

Dynamical and statistical properties of estimated high-dimensional ODE models: The case of the Lorenz'05 type II model