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The machine learning (ML) of phase transitions (PTs) has gradually become aneffective approach, which enables us to explore the nature of various PTs, morepromptly, in both equilibrium and non-equilibrium systems. Unlike equilibriumsystems, non-equilibrium systems display more complicated and diverse features,due to the extra dimension of time, which are not readily tractable, boththeoretically and numerically. The combination of ML and the most renownednon-equilibrium model, the directed percolation (DP), has led to somesignificant findings. Here in this work, the ML technique will be applied tothe (1+1)-d even-offspring branching annihilating random walks (BAW), whoseuniversality class is not DP-like. The supervised learning of (1+1)-d BAW, viaconvolutional neural networks (CNN), results in a more accurate prediction ofthe critical point than the Monte Carlo (MC) simulation at the same systemsizes. The dynamic exponent \;$z$\; and the spatial correlation lengthcorrelation exponent \;$\nu_{\perp}$\ are also measured and found to beconsistent with the respective theoretical values. The unsupervised learning of(1+1)-d BAW, via autoencoder (AE), also gives rise to a transition point whichis the same as the critical point. The output of AE, through a single neuron,can be regarded as the order parameter of the system, being re-scaled properly.We therefore have the reason to believe that ML has an exciting applicationprospect in such reaction-diffusion systems as the BAW and DP.

Supervised and unsupervised learning of (1+1)-dimensional even-offspring branching annihilating random walks