When the equations of motion are obtained from the measurements via a numer-
ical procedure, we say that we have determined a surrogate model of the observed
system. The performance of surrogate models is often evaluated in terms of their
predictive capability, i.e. how well and for how long simulation time the predictions
of the surrogate models will approximate the real data. In this MSc thesis, we have
focused on another important aspect of the evaluation of surrogate models, namely,
we have studied how the dynamic properties (such as Lyapunov exponents) of sur-
rogate models differ from the original model i.e. system that is the source of the
numerical data. Specifically, we looked at how the dynamic and statistical prop-
erties of the surrogate models are affected by the amplitude of the white Gaussian
noise that was previously added to the numerical data to which the surrogate models
were fitted. We chose the 2005 Lorenz type II model as the source dynamical
system, which is an important toy model in the field of meteorology. Surrogate
models were obtained using the regression method SINDy, which is one of the
promising algorithms for finding alternative equations of motion from time series
of systems. We found that the dynamic properties of the surrogate models match
the dynamic properties of the original system reasonably well in the range of ampli-
tudes of the data-added noise, where the surrogate models do not generate divergent
(unbounded) trajectories. Furthermore, we observed that as the amplitude of the
data-added noise increases, the dynamics of the surrogate models become less and
less chaotic. We also performed a variance analysis of the free parameters of the
surrogate models and found that, the free parameters of the model are mostly indi-
vidually dependent on small random perturbations of the input data.
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