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

Learning phase transitions from regression uncertainty: a new regression-based machine learning approach for automated detection of phases of matter

“…In recent years, the artificial neural network (NN) based machine learning techniques have stimulated the rapid development of automated data-driven approaches to investigate a wide range of physics problems [1][2][3]. As one of the central classes of problems in condensed matter physics and statistical physics, classifying phases of matter and identifying phases transitions is a major focus of applying both generative machine learning [4][5][6][7][8] and discriminative machine learning [9][10][11][12][13][14][15][16][17][18][19][20]. Particularly, approaches utilizing the power of NNs in performing classification discriminative tasks were developed and succeeded in providing data-driven evidence on the existence of various phase transitions [9,10], including the phase transitions associated with nonequilibrium self-propelled particles [11,12], topological defects [13][14][15][16], many-body localization [17,18], strongly correlated fermions [19,20], etc.…”

“…As one of the central classes of problems in condensed matter physics and statistical physics, classifying phases of matter and identifying phases transitions is a major focus of applying both generative machine learning [4][5][6][7][8] and discriminative machine learning [9][10][11][12][13][14][15][16][17][18][19][20]. Particularly, approaches utilizing the power of NNs in performing classification discriminative tasks were developed and succeeded in providing data-driven evidence on the existence of various phase transitions [9,10], including the phase transitions associated with nonequilibrium self-propelled particles [11,12], topological defects [13][14][15][16], many-body localization [17,18], strongly correlated fermions [19,20], etc. And besides the widely-involved classification tasks, there is yet another fundamental class of discriminative tasks that machine learning can efficiently dealt with, namely, regression tasks [21].…”

Learning Phase Transitions from Regression Uncertainty

“…As one of the central classes of problems in condensed matter physics, classifying phases of matter and identifying phases transitions is a major focus of applying machine learning. In particular, a considerable number of approaches utilizing the power of NNs in performing classification tasks have been developed and succeeded in providing data-driven evidence on the existence of various phase transitions [4,5], such as the phase transitions associated with nonequilibrium self-propelled particles [6,7], topological defects [8][9][10][11], many-body localization [12,13], strongly correlated fermions [14,15], etc. And besides the widely-involved classification tasks, there is yet another fundamental class of tasks that can be dealt with efficiently by modern machine learning techniques, namely, regression tasks [16].…”

“…1(b)]. By utilizing this "hidden" information, we develop a new unsupervised machine learning approach dubbed "learning from regression uncertainty" (LFRU) for automated detection of phases of matter, with the core working horse being an NN performing regression tasks instead of classification tasks as in various related machine learning approaches developed so far [4][5][6][7][8][9][10][11][12][13][14][15][41][42][43][44][45]. This is achieved by revealing an intrinsic connection between regression uncertainty and response properties of the system under consideration [cf.…”

Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in deformable particles

“…However, a firm confirmation within this approach is still difficult, partially due to the possibly enormous value of the hexatic correlation length [12] and also the fact that other complicated defects, such as vacancies and grain boundaries, might appear near the phase transitions [27][28][29]. Noticing that machine learning techniques have emerged in recent years as an efficient tool to investigate various problems on phase transitions [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], this thus raises the intriguing opportunity to develop new tools based on these powerful techniques to reveal new physical insights into these open questions, in particular, the ones concerning the existence of the intermediate hexatic phase and the fundamental nature of its associated phase transitions, especially the possible critical scaling behavior.…”