Unsupervised Discovery of Phase Transitions in 3D Swarmalators via LSTM Autoencoders

Swarmalator systems, which couple oscillator synchronization with active particle motion, exhibit a rich tapestry of emergent behaviors—from static clusters to breathing Chimeras—that often elude classification via traditional, heuristic order parameters. In this work, we present a novel, fully unsupervised deep learning framework designed to discover and map these thermodynamic phases directly from raw 3D trajectories, eliminating human bias. Our approach leverages a physics-informed preprocessing step that transforms coordinates into pairwise invariants, ensuring robustness against rotational and permutational symmetries. These features drive an LSTM Autoencoder, which learns to compress complex temporal dynamics into a low-dimensional latent manifold. Through latent space clustering, we successfully reconstructed the system’s phase diagram ($J$ vs $K$), demonstrating the model's ability to disentangle dynamic states that are geometrically similar but temporally distinct. Finally, we show how this self-learned knowledge can be distilled into a real-time classifier, offering a powerful, generalized tool for the automated analysis of active matter.