Deciphering Dynamical Nonlinearities in Short Time Series Using Recurrent Neural Networks
This work addresses the problem of identifying chaotic processes in short time series for researchers in fields like physics and biology, though it is incremental as it builds on existing surrogate testing methods.
The study tackled the challenge of detecting dynamical nonlinearities in short time series by proposing a recurrent neural network classification framework that eliminates the need for discriminant statistics and handles multiple realizations. Results showed classifier accuracy markedly higher than 50% for chaotic processes and around 50% for nonlinearly correlated noise, demonstrating its usefulness for short experimental data.
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.