Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data

The intrinsic dimension (ID) is a powerful tool to detect and quantify correlations from data. Recently, it has been successfully applied to study statistical and many-body systems in equilibrium, yet its application to systems away from equilibrium remains largely unexplored. Here we study the ID of nonequilibrium growth dynamics data, and show that even after reducing these data to binary form, their binary intrinsic dimension (BID) retains essential physical information. Specifically, we find that, akin to the surface width, it exhibits Family-Vicsek dynamical scaling-a fundamental feature to describe universality in surface roughness phenomena. These findings highlight the ability of the BID to correctly discern key properties and correlations in nonequilibrium data, and open an avenue for alternative characterizations of out-of-equilibrium dynamics.