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.

13 pages, 7 figures

References in corpus (14)

• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• Big Data of Materials Science - Critical Role of the Descriptor
• Machine learning for molecular simulation
• Learning phase transitions by confusion
• Nearsightedness of Electronic Matter
• Opportunities and Challenges for Machine Learning in Materials Science
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Machine learning vortices at the Kosterlitz-Thouless transition
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Arrested phase separation in double-exchange models: machine-learning enabled large-scale simulation
• Few-shot machine learning in the three-dimensional Ising model
• Scalable neural networks for the efficient learning of disordered quantum systems
• Convolutional neural networks for large-scale dynamical modeling of itinerant magnets
• 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