Graph neural networks unveil universal dynamics in directed percolation

Recent advances in statistical physics highlight the significant potential of machine learning for phase transition recognition. This study introduces a deep learning framework based on graph neural network to investigate non-equilibrium phase transitions, specifically focusing on the directed percolation process. By converting lattices with varying dimensions and connectivity schemes into graph structures and embedding the temporal evolution of the percolation process into node features, our approach enables unified analysis across diverse systems. The framework utilizes a multi-layer graph attention mechanism combined with global pooling to autonomously extract critical features from local dynamics to global phase transition signatures. The model successfully predicts percolation thresholds without relying on lattice geometry, demonstrating its robustness and versatility. Our approach not only offers new insights into phase transition studies but also provides a powerful tool for analyzing complex dynamical systems across various domains.