TY  - JOUR
T1  - Hybrid Deep Learning-Enhanced Topological Data Analysis Framework for Real-Time Detection and Classification of Chaotic Attractors
AU  - Bhardwaj, Neha
AU  - Sıngh, Rashmı
AU  - Nishad, Dinesh
AU  - Khalid, Saifullah
PY  - 2025
DA  - November
Y2  - 2025
DO  - 10.51537/chaos.1705535
JF  - Chaos Theory and Applications
JO  - CHTA
PB  - Akif AKGÜL
WT  - DergiPark
SN  - 2687-4539
SP  - 273
EP  - 283
VL  - 7
IS  - 3
LA  - en
AB  - 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.
KW  - Nonlinear dynamics
KW  - Topological data
analysis
KW  - Deep learning
KW  - Chaotic attractors
KW  - Persistent homology
KW  - Real-time processing
CR  - Almazova, N., G. D. Barmparis, and G. P. Tsironis, 2021 Chaotic
dynamical systems and neural network configurations: A review.
IEEE Access 9: 123456–123470.
CR  - Biamonte, J., P.Wittek, N. Pancotti, P. Rebentrost, N.Wiebe, et al.,
2017 Quantum machine learning. Nature 549: 195–202.
CR  - Celletti, A., C. Gales, V. Rodríguez-Fernández, and M. Vasile, 2022
Classification of regular and chaotic motions in hamiltonian
systems with deep learning. Scientific Reports 12: 839.
CR  - Chen, X., P. Yadav, R. Singh, and S. M. N. Islam, 2023 Es structure
based on soft j-subset. Mathematics 11: 853.
CR  - Cohen-Steiner, D., H. Edelsbrunner, and J. Harer, 2007 Stability of
persistence diagrams. Discrete & Computational Geometry 37:
103–120.
CR  - Dean, J. and S. Ghemawat, 2008 Mapreduce: Simplified data processing
on large clusters. Communications of the ACM 51: 107–
113.
CR  - Gidea, M. and Y. Katz, 2018 Topological data analysis of financial
time series: Landscapes of crashes. Physica A: Statistical
Mechanics and its Applications 491: 820–834.
CR  - Kavuran, G., 2022 When machine learning meets fractional-order
chaotic signals: Detecting dynamical variations. Chaos, Solitons
& Fractals 160: 111908.
CR  - Kohavi, R., 1995 A study of cross-validation and bootstrap for
accuracy estimation and model selection. International Joint
Conference on Artificial Intelligence 14: 1137–1143.
CR  - LeCun, Y., Y. Bengio, and G. Hinton, 2015 Deep learning. Nature
521: 436–444.
CR  - Leykam, D. and D. G. Angelakis, 2023 Topological data analysis
and machine learning. Advances in Physics: X 8.
CR  - Majumdar, S. and A. K. Laha, 2020 Clustering and classification of
time series using topological data analysis with applications to
finance. Expert Systems with Applications 162: 113868.
CR  - Mittal, S. and R. Singh, 2017 Fuzzy g-semi open sets and fuzzy
g-semi continuous functions. Journal of Information and Optimization
Sciences 38: 1039–1046.
CR  - Myers, A., E. Munch, and F. A. Khasawneh, 2019 Persistent homology
of complex networks for dynamic state detection. Phys. Rev.
E 100: 022314.
CR  - Rabadán, R. and A. J. Blumberg, 2019 Topological Data Analysis for
Genomics and Evolution: Topology in Biology. Cambridge University
Press.
CR  - Röhm, A., D. Gauthier, and I. Fischer, 2021 Model-free inference
of unseen attractors: Reconstructing phase space features from
a single noisy trajectory using reservoir computing. Chaos 31:
123110.
CR  - Singh, R., 2017 Symmetric relations on ix. American Institute of
Physics Proceedings 1897: 020038.
CR  - Singh, R., N. Bhardwaj, and S. M. N. Islam, 2023 The role of mathematics
in data science: Methods, algorithms, and computer
programs. In Advanced Mathematical Applications in Data Science,
pp. 1–23, Springer.
CR  - Singh, R., N. Bhardwaj, and S. M. N. Islam, 2024a Applications of
mathematical techniques to artificial intelligence: Mathematical
methods, algorithms, computer programming and applications.
In Advances on Mathematical Modeling and Optimization with Its
Applications, pp. 152–169, Springer.
CR  - Singh, R., K. Khurana, and P. Khandelwal, 2024b Decision-making
in mask disposal techniques using soft set theory. In Computational
Intelligence, Lecture Notes in Electrical Engineering, volume
968, pp. 649–661, Springer, Singapore.
CR  - Singh, R., A. Kumar Umrao, and J. T. Pandey, 2020 k, t, dproximities
in rough set. WSEAS Transactions on Mathematics
19: 498–502.
CR  - Singh, R. and A. K. Umrao, 2019 On finite order nearness in soft
set theory. WSEAS Transactions on Mathematics 18: 118–122.
CR  - Smith, A. D., P. Dlotko, and V. M. Zavala, 2021 Topological data
analysis: Concepts, computation, and applications in chemical
engineering. Computers & Chemical Engineering 146: 107202.
CR  - Takens, F., 1981 Detecting strange attractors in turbulence. Dynamical
Systems and Turbulence, Warwick 1980 pp. 366–381.
CR  - Uray, M., B. Giunti, M. Kerber, and S. Huber, 2024 Topological
data analysis in smart manufacturing: State of the art and future
directions. Journal of Manufacturing Systems 76: 75–91.
CR  - Wu, G.-C., Z.Wu, andW. Zhu, 2024 Data-driven discrete fractional
chaotic systems, new numerical schemes and deep learning.
Chaos 34: 013101.
CR  - Yadav, P. and R. Singh, 2021 On soft sets based on es structure, elalgebra.
In 2021 5th International Conference on Information Systems
and Computer Networks (ISCON), pp. 1–6.
CR  - Young, C. D. and M. Graham, 2022 Deep learning delay coordinate
dynamics for chaotic attractors from partial observable data.
Physical Review E 107: 034215.
CR  - Zhu, X., Y. Wang, and Y. Wang, 2022 Chaotic physical security
scheme based on variational auto-encoders. Optics Communications
505: 127512.
CR  - Zia, A., A. Khamis, and J. e. a. Nichols, 2024 Topological deep learning:
a review of an emerging paradigm. Artificial Intelligence
Review 57: 77.
UR  - https://doi.org/10.51537/chaos.1705535
L1  - https://dergipark.org.tr/en/download/article-file/4898291
ER  -