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Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…
Neural network based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized or topological…
Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…
Despite their importance in a wide variety of applications, the estimation of ionization cross sections for large molecules continues to present challenges for both experiment and theory. Machine learning algorithms have been shown to be an…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder -- either random bonds or random fields -- we show that a critical percolation structure forms in an early stage and…
We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
In an artificial 3D percolation nano medium, the clusters filled by the Ising magnets give rise to a topologically nontrivial magnetic structure, leading to new features of the ferromagnetic phase transition without an external magnetic…
The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper…
Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical…
Recently, machine learning has been applied successfully for identifying phases and phase transitions of the Ising models. The continuous phase transition is characterized by spontaneous symmetry breaking, which can not be detected in…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
In this study, we use machine learning to classify and interpolate the phase structure of the Vicsek flocking model across the three-dimensional parameter space $(\eta,\rho,v_0)$. We construct a dataset of simulated parameter points and…
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…
Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…
We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier…
We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties of the stationary measure from within a…