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We establish an explicit data-driven criterion for identifying thesolid-liquid transition of two-dimensional self-propelled colloidal particlesin the far from equilibrium parameter regime, where the transition pointspredicted by different conventional empirical criteria for melting and freezingdiverge. This is achieved by applying a hybrid machine learning approach thatcombines unsupervised learning with supervised learning to analyze over onemillion of the system's configurations in the nonequilibrium parameter regime.Furthermore, we establish a generic data-driven evaluation function, accordingto which the performance of different empirical criteria can be systematicallyevaluated and improved. In particular, by applying this evaluation function, weidentify a new nonequilibrium threshold value for the long-time diffusioncoefficient, based on which the predictions of the corresponding empiricalcriterion are greatly improved in the far from equilibrium parameter regime.These data-driven approaches provide a generic tool for investigating phasetransitions in complex systems where conventional empirical ones facedifficulties.

Data-driven criterion for the solid-liquid transition of two-dimensional self-propelled colloidal particles far from equilibrium