We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of two-dimensional hard-disk and three-dimensional hard-sphere systems as well as liquid-gas phase separation in a patchy colloid model. As we demonstrate, PCA autonomously discovers order-parameter-like quantities that report on phase transitions, mitigating the need for a priori construction or identification of a suitable order parameter—thus streamlining the routine analysis of phase behavior. In a companion paper, we further develop the method established here to explore the detection of phase transitions in various model systems controlled by compositional demixing, liquid crystalline ordering, and non-equilibrium active forces.
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We outline how principal component analysis can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to study (1) the nonequilibrium random organization (RandOrg) model that exhibits a phase transition from quiescent to steady-state behavior as a function of density, (2) orientationally and positionally driven equilibrium phase transitions for hard ellipses, and (3) a compositionally driven demixing transition in the non-additive binary Widom-Rowlinson mixture.
