Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The International Journal of Multiphysics

Machine Learning-Driven Prediction of Phase Transitions in Advanced Condensed Matter Systems: A Review of Methods, Applications, and Open Challenges

Amit Ghas et al.

Published Dec 31, 2021• 0 citations
OpenAlex

Abstract

The identification and characterization of phase transitions is one of the oldest and most central problems in condensed matter physics, traditionally approached through order parameters, free-energy expansions, renormalization-group analysis, and direct numerical simulation. Over the past decade, machine learning (ML) has emerged as a complementary and, in some regimes, transformative methodology for this task. Supervised classifiers can learn to distinguish phases directly from raw configurations without an a priori order parameter; unsupervised and self-supervised techniques such as principal component analysis, autoencoders, and learning-by-confusion can locate transition points with minimal or no labeled data; and generative and variational architectures, including neural-network quantum states, now approximate ground-state wavefunctions of strongly correlated systems well beyond the reach of exact diagonalization. This paper reviews the theoretical foundations of phase transitions relevant to machine-learning applications, surveys the principal families of algorithms used to detect and classify phases, and examines their application across classical spin systems, percolation, topological and quantum phases, strongly correlated electron systems, and experimentally measured spectroscopic data. Representative case studies are discussed, including convolutional and graph-neural-network classifiers of lattice configurations, explainable-ML detection of thermodynamic transitions in photoemission spectra, and deep-learning-guided discovery of high-temperature superconductors. The review closes with a critical discussion of persistent challenges interpretability, data scarcity in correlated-electron experiments, generalization across Hamiltonians, and the reliability of learned order parameters near criticality and outlines directions for future research, including physics-informed architectures, uncertainty quantification, and closed-loop integration with autonomous experimentation.

Related papers

机器学习在相变中的应用

Yuxiang Yang, Wei Li, Jianmin Shen +5 more

Neural networks in machine learning are highly capable of classifying data and recognizing graphics, and have been widely used in statistical physics, particularly in phase transitions. In this paper, we review recent developments in machine learning algorithms in the application of primary phase transition models. We first introduce the background of modern machine learning algorithms and related pioneering work in equilibrium phase transitions. Second, by taking directed percolation as an example of a typical non-equilibrium phase transition model, we present some of the latest research findings of our group. The research involves supervised, unsupervised, and semi-supervised learning for classifying phases, predicting critical points, and measuring critical exponents. Thereafter, we elaborate on related work on machine learning algorithms in phase transition research in quantum many-body theory, soft matter physics, and high-energy physics. Lastly, corresponding discussions and prospects are presented.

Zhongguo kexue. Wulixue Lixue Tianwenxue•May 1, 2023•1 citation

Machine Learning of Phases and Structures for Model Systems in Physics

Djénabou Bayo, Burak Çivitcioğlu, Joseph J. Webb +2 more

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as powerful tools to complement these standard approaches, offering valuable insights into phase and structure determination. Additionally, they have been shown to enhance the application of traditional methods. In this work, we review recent advancements in this area, with a focus on our contributions to phase and structure determination using supervised and unsupervised learning methods in several systems: (a) 2D site percolation, (b) the 3D Anderson model of localization, (c) the 2D $J_1$-$J_2$ Ising model, and (d) the prediction of large-angle convergent beam electron diffraction patterns.

arXiv:2409.03023•Journal of the Physical Society of Japan•Jan 10, 2025•7 citations

Vulnerability of Machine Learning Phases of Matter

Si Jiang, Sirui Lu, Dong-Ling Deng

Classifying different phases and the transitions between them is a major task in condensed matter physics. Machine learning, which has achieved dramatic success recently in a broad range of artificial intelligence applications, may bring an unprecedented perspective for this challenging task. In this paper, we study the robustness of this intriguing machine-learning approach to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial examples: adding a tiny amount of carefully-crafted noises, which are imperceptible to human eyes and ineffective to traditional methods, into the original legitimate data obtained from numerical simulations or real experiments will cause the classifiers to make incorrect predictions at a notably high confidence level. Our results reveal a novel vulnerability aspect in applying machine learning techniques to condensed matter physics, which provides a valuable guidance for both theoretical and experimental future studies along this direction.

•Oct 29, 2019•3 citations

Phase determination with and without deep learning

Burak Çivitcioğlu, Rudolf A. Römer, A. Honecker

Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the J_{1}-J_{2} Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.

arXiv:2403.09786•Physical review. E•Feb 18, 2025•7 citations

Discovering phase transitions with unsupervised learning

Lei Wang

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in large data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many-body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low-dimensional representations of the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds physical concepts such as the order parameter and structure factor to be indicators of a phase transition. We discuss the future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.

arXiv:1606.00318•Physical review. B./Physical review. B•Nov 2, 2016•617 citations

Unveiling phase transitions with machine learning

Askery Canabarro, F. F. Fanchini, André Luiz Malvezzi +2 more

The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest-neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor interactions are introduced. All our results rely on few- and low-dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.

arXiv:1904.01486•Physical review. B./Physical review. B•Jul 22, 2019•96 citations
The identification and characterization of phase transitions is one of the oldest and most central problems in condensed matter physics, traditionally approached through order parameters, free-energy expansions, renormalization-group analysis, and direct numerical simulation. Over the past decade, machine learning (ML) has emerged as a complementary and, in some regimes, transformative methodology for this task. Supervised classifiers can learn to distinguish phases directly from raw configurations without an a priori order parameter; unsupervised and self-supervised techniques such as principal component analysis, autoencoders, and learning-by-confusion can locate transition points with minimal or no labeled data; and generative and variational architectures, including neural-network quantum states, now approximate ground-state wavefunctions of strongly correlated systems well beyond the reach of exact diagonalization. This paper reviews the theoretical foundations of phase transitions relevant to machine-learning applications, surveys the principal families of algorithms used to detect and classify phases, and examines their application across classical spin systems, percolation, topological and quantum phases, strongly correlated electron systems, and experimentally measured spectroscopic data. Representative case studies are discussed, including convolutional and graph-neural-network classifiers of lattice configurations, explainable-ML detection of thermodynamic transitions in photoemission spectra, and deep-learning-guided discovery of high-temperature superconductors. The review closes with a critical discussion of persistent challenges interpretability, data scarcity in correlated-electron experiments, generalization across Hamiltonians, and the reliability of learned order parameters near criticality and outlines directions for future research, including physics-informed architectures, uncertainty quantification, and closed-loop integration with autonomous experimentation.
Neural networks in machine learning are highly capable of classifying data and recognizing graphics, and have been widely used in statistical physics, particularly in phase transitions. In this paper, we review recent developments in machine learning algorithms in the application of primary phase transition models. We first introduce the background of modern machine learning algorithms and related pioneering work in equilibrium phase transitions. Second, by taking directed percolation as an example of a typical non-equilibrium phase transition model, we present some of the latest research findings of our group. The research involves supervised, unsupervised, and semi-supervised learning for classifying phases, predicting critical points, and measuring critical exponents. Thereafter, we elaborate on related work on machine learning algorithms in phase transition research in quantum many-body theory, soft matter physics, and high-energy physics. Lastly, corresponding discussions and prospects are presented.
The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as powerful tools to complement these standard approaches, offering valuable insights into phase and structure determination. Additionally, they have been shown to enhance the application of traditional methods. In this work, we review recent advancements in this area, with a focus on our contributions to phase and structure determination using supervised and unsupervised learning methods in several systems: (a) 2D site percolation, (b) the 3D Anderson model of localization, (c) the 2D J1J_1J1​-J2J_2J2​ Ising model, and (d) the prediction of large-angle convergent beam electron diffraction patterns.
Classifying different phases and the transitions between them is a major task in condensed matter physics. Machine learning, which has achieved dramatic success recently in a broad range of artificial intelligence applications, may bring an unprecedented perspective for this challenging task. In this paper, we study the robustness of this intriguing machine-learning approach to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial examples: adding a tiny amount of carefully-crafted noises, which are imperceptible to human eyes and ineffective to traditional methods, into the original legitimate data obtained from numerical simulations or real experiments will cause the classifiers to make incorrect predictions at a notably high confidence level. Our results reveal a novel vulnerability aspect in applying machine learning techniques to condensed matter physics, which provides a valuable guidance for both theoretical and experimental future studies along this direction.
Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the J_{1}-J_{2} Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.
Unsupervised learning is a discipline of machine learning which aims at discovering patterns in large data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many-body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low-dimensional representations of the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds physical concepts such as the order parameter and structure factor to be indicators of a phase transition. We discuss the future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.
The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest-neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor interactions are introduced. All our results rely on few- and low-dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.