Machine learning for structure-property relationships: Scalability and limitations

Abstract

We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of many-body systems. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide and conquer approach, and the locality of physical properties is key to partitioning the system into sub-domains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. The two-dimensional Ising model is used to demonstrate the proposed framework. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed.

arXiv comment13 pages, 7 figures

References in corpus (48)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• On representing chemical environments
• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
• Moment Tensor Potentials: a class of systematically improvable interatomic potentials
• Machine learning phases of matter
• Big Data of Materials Science - Critical Role of the Descriptor
• Machine learning for molecular simulation
• DScribe: Library of Descriptors for Machine Learning in Materials Science
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Nearsightedness of Electronic Matter
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Opportunities and Challenges for Machine Learning in Materials Science
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Machine Learning Topological States
• Quantum Loop Topography for Machine Learning
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Machine learning vortices at the Kosterlitz-Thouless transition
• Probing many-body localization with neural networks
• Machine learning out-of-equilibrium phases of matter
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Machine Learning for Condensed Matter Physics
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Identifying polymer states by machine learning
• Super-resolving the Ising model with convolutional neural networks
• Extensive deep neural networks for transferring small scale learning to large scale systems
• Supervised learning magnetic skyrmion phases
• Thermodynamics and Feature Extraction by Machine Learning
• Learning the Ising Model with Generative Neural Networks
• Machine learning for molecular dynamics with strongly correlated electrons
• Is Deep Learning a Renormalization Group Flow?
• Machine Learning Application to Two-Dimensional Dzyaloshinskii-Moriya Ferromagnets
• Arrested phase separation in double-exchange models: machine-learning enabled large-scale simulation
• Few-shot machine learning in the three-dimensional Ising model
• Machine learning electron correlation in a disordered medium
• Scalable neural networks for the efficient learning of disordered quantum systems
• Machine learning techniques to construct detailed phase diagrams for skyrmion systems
• Convolutional neural networks for large-scale dynamical modeling of itinerant magnets
• Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations
• Machine learning predictions for local electronic properties of disordered correlated electron systems
• Supervised learning of few dirty bosons with variable particle number
• Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets

Cited by in corpus (5)

• Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems
• Machine learning approach for vibronically renormalized electronic band structures
• Challenges and opportunities in the supervised learning of quantum circuit outputs