ChaosNet-Transformer: A Physics-Informed Deep Learning Framework for Predicting and Synchronizing High-Dimensional Chaotic Dynamical Systems
DOI:
https://doi.org/10.64366/adajisr.v3i3.584Keywords:
Chaotic Systems; Deep Learning; Lyapunov Exponents; Koopman Operator; Reservoir Computing; Transformer Architecture; Time Series Prediction; Chaos SynchronizationAbstract
Predicting and synchronizing high-dimensional chaotic dynamical systems remains a fundamental challenge in artificial intelligence and nonlinear science because chaotic trajectories exhibit strong sensitivity to initial conditions and rapid error divergence. This study proposes ChaosNet-Transformer (CNT), a physics-informed deep learning framework that combines Lyapunov-regularized temporal attention, Reservoir-Enhanced Embedding, and a Koopman Linearization Module to improve chaotic time-series prediction while preserving the underlying dynamical structure. CNT is evaluated on six benchmark systems, namely Lorenz-63, Rössler, Mackey-Glass, Chen-Lu, Qi Hyperchaos, and the Kuramoto-Sivashinsky system. The proposed model is compared with Echo State Network (ESN), Next-Generation Reservoir Computing (NG-RC), FEDformer, and Chaos-Informed LSTM (CI-LSTM) using Valid Prediction Time (VPT) measured in Lyapunov Time. Experimental results show that CNT achieves the highest VPT across all benchmark systems and consistently outperforms the strongest baseline methods. The synchronization experiment further demonstrates that CNT produces lower synchronization error than ESN and FEDformer under comparable coupling conditions. Ablation results confirm that Reservoir-Enhanced Embedding, Lyapunov regularization, and Koopman-based latent linearization each contribute to the model performance. These findings indicate that integrating Transformer-based sequence modeling with physics-informed constraints can improve the prediction and synchronization of chaotic dynamical systems.
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Copyright (c) 2026 Wanayumini Wanayumini, Sabir Ramadhan, Miftahul Jannah, Arya Agung Pratama, Tiara Rahmadhani Samosir, Novi Rahmawati
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