Deciphering Dynamical Nonlinearities in Short Time Series Using Recurrent Neural Networks

TL;DR

This paper introduces a recurrent neural network framework that classifies short time series to detect dynamical nonlinearities, eliminating the need for discriminant statistics and improving analysis of chaotic systems.

Contribution

The study presents a novel RNN-based classification method that directly uses raw short time series, enhancing the detection of nonlinear dynamics without relying on traditional discriminant statistics.

Findings

Classifier accuracy > 50% for chaotic regimes

Performance around 50% for nonlinear noise, similar to random chance

Framework effectively identifies nonlinearities in short time series

Abstract

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.