Hybrid Deep Learning-Enhanced Topological Data Analysis Framework for Real-Time Detection and Classification of Chaotic Attractors

Year 2025, Volume: 7 Issue: 3, 273 - 283, 30.11.2025

Rashmı Sıngh , Dinesh Nishad , Neha Bhardwaj , Saifullah Khalid

https://doi.org/10.51537/chaos.1705535

Abstract

We introduce a hybrid framework that combines Topological Data Analysis (TDA) and deep learning architectures to detect and classify chaotic attractors in high-dimensional dynamical systems with real-time capability. Our approach exploits persistent homology to extract robust topological features, which are then processed by convolutional neural networks (CNNs) for pattern recognition. Our algorithm is both more accurate and more computationally efficient than state of the art tools such as traditional Lyapunov exponent analysis, phase space reconstruction methods and more recent deep learning tools Experimental results show that our algorithm is 95.8\% more accurate and 50ms faster to run on 1000-dimensional input data (95\% CI: [94.6\% 97.0\%]) than compared to state of the art methods, including the traditional Lyapunov exponent analysis and phase space reconstruction methods and more recent deep learning methods. The model is extremely resistant to noise, and its accuracy with signal-to-noise ratios as low as 15dB is 92.3\% with 1.5\% standard deviation. Extensive ablation experiments show that the hybrid method is better than the single TDA (82.4\% accuracy) and deep learning (78.9\% accuracy) modules, which proves the synergy advantage. Performance analysis O(n log n) computational complexity and linear scaling properties The performance analysis has a 3.2x speedup over traditional algorithms and has a 45 percent memory reduction. The study is an improvement on nonlinear dynamics as it offers an efficient, scalable, and robust algorithm to identify chaotic system dynamics in real-time and can be applied in climate modeling, financial markets, and neurological signal processing.

Keywords

Nonlinear dynamics , Topological data analysis , Deep learning , Chaotic attractors , Persistent homology , Real-time processing

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