  Surrogate testing techniques have been used widely to investigate the
presence of dynamical nonlinearities, an essential ingredient of deterministic
chaotic processes. Traditional surrogate testing subscribes to statistical
hypothesis testing and investigates potential differences in discriminant
statistics between the given empirical sample and its surrogate counterparts.
The choice and estimation of the discriminant statistics can be challenging
across short time series. Also, conclusion based on a single empirical sample
is an inherent limitation. The present study proposes a recurrent neural
network classification framework that uses the raw time series obviating the
need for discriminant statistic while accommodating multiple time series
realizations for enhanced generalizability of the findings. The results are
demonstrated on short time series with lengths (L = 32, 64, 128) from
continuous and discrete dynamical systems in chaotic regimes, nonlinear
transform of linearly correlated noise and experimental data. Accuracy of the
classifier is shown to be markedly higher than >> 50% for the processes in
chaotic regimes whereas those of nonlinearly correlated noise were around ~50%
similar to that of random guess from a one-sample binomial test. These results
are promising and elucidate the usefulness of the proposed framework in
identifying potential dynamical nonlinearities from short experimental time
series.
