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

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.