Discovering phase transitions with unsupervised learning

By Lei Wang. 2016

509 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/24f8b9d8b9ec39322a6e141f5bd99f2e947fd22e

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In Artificial Intelligence

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “In recent years, it has been applied to condensed matter physics for phase transitions [194, 195], design of a magneto-optical trap [196] and other aspects [197].”
Machine Learning Phases of Strongly Correlated Fermions (2016, unknown): “Further distribution of this work must maintain attribution to the author(s) and the published article ’ s title, journal citation, and DOI. matter in classical Ising-type models, effectively locating critical temperatures at which transitions between phases take place [11,12].”
Explainable Machine Learning for Scientific Insights and Discoveries (2019, methodology): “similar way, [83] and [84] use principal component analysis and the derived interpretable principal components for exploration of different phases, phase-transition, and crossovers in classical spin models.”
Machine learning \& artificial intelligence in the quantum domain (2017, methodology): “In an extensive, and complementary work (Wang, 2014), the authors rely on the powerful technique of “qubitization” (Low and Chuang, 2016), and optimize the goal of actually producing the best-fit parameters β.”
Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders (2017, methodology): “Phase transitions were found in an unsupervised manner using principle component analysis [24, 25].”
Solving the quantum many-body problem with artificial neural networks (2016, background): “Very recently, applications of neural network to the study of physical phenomena have been introduced [18–20].”
Neural-network quantum state tomography (2017, background): “Applications to quantum many-body systems have been put forward last year, to classify phases of matter 3–6 , and to improve the simulation of classical 7,8 and quantum 9 systems.”
Quantum Entanglement in Neural Network States (2017, background): “Exciting progress has been made in identifying quantum phases and transitions among them (either conventional symmetry-broken [33, 35, 37, 38] or topological phases [32]), modeling thermodynamic observables [36], constructing decoders for topological codes [39], accelerating Monte Carlo simulations…”
Neural Network Renormalization Group (2018, background): “[27] Lei Wang, “Discovering phase transitions with unsupervised learning,” Physical Review B 94, 195105 (2016), arXiv:1606.”
Machine learning quantum phases of matter beyond the fermion sign problem (2016, background): “Neural networks have recently been demonstrated capable of discriminating between classical phases of matter, through direct training on Monte Carlo conﬁgurations [14, 15].”