Deep learning for classifying dynamical states from time series via recurrence plots

TL;DR

We address the challenge of identifying dynamical states from time series without relying on computationally intensive recurrence measures. Our approach uses images of recurrence plots fed into a dual-branch CNN (DBResNet-50) built on ResNet-50 to learn discriminative RP features, achieving high accuracy across seven dynamical regimes and generalizing to experimental and observational data. The results show robust classification on synthetic, circuit, astronomical, and climate data, with the method capturing mixed deterministic-stochastic dynamics and offering fast, scalable state classification. This RP-image-based framework provides a practical, interpretable alternative to feature-based RQA, with potential extensions including multi-rate ensembles and segmentation-based dynamical transition detection.

Abstract

Recurrence Quantification Analysis (RQA) is a widely used method for capturing the dynamical structure embedded in time series data, relying on the analysis of recurrence patterns in the reconstructed phase space via recurrence plots (RPs). Although RQA proves effective across a range of applications, it typically requires the computation of multiple quantitative measures, making it both computationally intensive and sensitive to parameter choices. In this study, we adopt an alternative approach that bypasses computation of recurrence measures by directly using images of RP as input to a deep learning model. We propose a new dual-branch deep learning model named DBResNet-50 built on the ResNet-50 architecture. We compare its performance with standard ResNet-50 and MobileNetV2. Our DBResNet-50 model, trained exclusively on simulated time series, accurately classifies seven dynamical regimes: periodic, quasi-periodic, chaotic, hyperchaotic, white noise, pink noise, and red noise. Further, to assess its generalizability, we test the trained model on RP images generated from standard dynamical systems not included in the training set, as well as experimental datasets from a Chua circuit, X-ray light curves from the black-hole system GRS 1915+105, and observational light curves of the variable stars AC Her, SX Her, and Chi Cygni. In all cases, DBResNet-50 outperforms the baselines and correctly predicts the known dynamics of these systems. The model further used to infers the relative contributions of deterministic and stochastic components within a signal, as observed in temperature data from Ladakh and Ranchi. These results demonstrate the robustness and versatility of our deep learning framework and underscore the potential of RP image-based models as fast, accurate, and scalable tools for classifying dynamical states in both synthetic and real-world time series data.

Figures (6)

• Figure 1: Classification of time series. Schematic representation of the proposed methodology for classifying time series using RPs as input to the proposed deep learning model. (a) We begin by selecting a normalized time series from some simulated dynamical systems and noise generator as listed in Table \ref{['tab:dynamical_systems']}. (b) The phase space of the selected time series is reconstructed using Takens’ embedding theorem. (c) A recurrence plot is then generated from the embedded trajectory using a suitable recurrence threshold $\epsilon$. (d) The resulting RP is resized and used as the input to the deep learning model. In this model, ResNet-50 helps to extract features from RP. Its output is processed through two parallel branches. The standard branch captures high-level spatial features, and the directional branch uses multiple early feature maps from the ResNet 50 pipeline, which are shown by the two arrows drawn from the mid-layers of ResNet 50. The outputs from both branches are concatenated and passed through a dense layer. Finally, a softmax layer generates class wise probabilities, from which the most probable dynamical state is identified. For example, if the input time series is chaotic, the output layer assigns a higher probability to the chaotic class.
• Figure 2: Representative recurrence plots from all the seven classes. These plots are obtained from the univariate time series corresponding to the following seven classes: (a) Periodic (Lorenz 4D), (b) Quasiperiodic, (c) Chaotic (Lorenz 4D), (d) Hyperchaotic (Chen 4D), (e) Red Noise, (f) White Noise, and (g) Pink Noise.
• Figure 3: Confusion matrices. Confusion matrices showing classification performance of (a) DBResNet-50 (b) ResNet-50, (c) MobileNetV2 models on datasets generated by simulating models of Table \ref{['tab:dynamical_systems']} at parameter sets different from training but show same type dynamical behaviour. Diagonal cells indicate correctly classified recurrence plots, while off-diagonal cells indicate misclassifications. It is evident that DBResNet-50 is the best-performing model, as nearly all samples lie along the diagonal.
• Figure 4: Experimental data from Chua’s circuit. (a) Time series obtained experimentally from Chua’s circuit. The red lines indicate the cropped portions of the time series at 2,500 and 5,000 data points, while the entire plot corresponds to 10,000 points. (b) Corresponding RP, with the red lines highlighting the regions in the RP corresponding to the cropped portions shown in (a).
• Figure 5: X-ray light curves from the black hole GRS 1915+105. (a) Light curve data from category $\gamma$ and (b) its corresponding recurrence plot. (c) Light curve data from category $\chi$ and (d) its corresponding recurrence plot.