Characterizing the latent topology of chaotic networks through recurrent neural architectures informed by synchronization manifolds

Understanding the collective behavior of chaotic oscillator networks requires uncovering the relationship between their dynamics and underlying connectivity. In this work, we propose a data-driven framework that uses Long Short-Term Memory (LSTM) networks to infer network topology using synchronization-based information derived from synchronization error, cross-correlation, and phase synchronization. These features provide complementary information about the collective dynamics and allow the model to learn relevant representations of the system across different coupling regimes. The results show that LSTM architectures can reconstruct hidden connectivity patterns from time-series data, achieving the best performance at intermediate coupling strengths. This approach offers a model-independent methodology for identifying interactions in complex oscillator networks by combining nonlinear dynamics with machine learning-based inference.