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

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.