Identifying internal patterns in (1+1)-dimensional directed percolation using neural networks

In this paper we present a neural network-based method for the automatic detection of phase transitions and classification of hidden percolation patterns in a (1+1)-dimensional replication process. The proposed network model is based on the combination of CNN, TCN and GRU networks, which are trained directly on raw configurations without any manual feature extraction. The network reproduces the phase diagram and assigns phase labels to configurations. It shows that deep architectures are capable of extracting hierarchical structures from the raw data of numerical experiments.