Scalable neural networks for the efficient learning of disordered quantum systems

Abstract

Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [K. Mills et al., Chem. Sci. 10, 4129 (2019)] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pre-training performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.

arXiv comment12 pages, 11 figures

References in corpus (26)

• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Machine Learning Unifies the Modelling of Materials and Molecules
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• How to represent crystal structures for machine learning: towards fast prediction of electronic properties
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Incorporating long-range physics in atomic-scale machine learning
• Deep learning and the Schrödinger equation
• Machine Learning for Quantum Matter
• Deep Learning and Density Functional Theory
• Chemical diversity in molecular orbital energy predictions with kernel ridge regression
• Deep learning the Hohenberg-Kohn maps of Density Functional Theory
• Collective dynamics and expansion of a Bose-Einstein condensate in a random potential
• Super-resolving the Ising model with convolutional neural networks
• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• Extensive deep neural networks for transferring small scale learning to large scale systems
• Transfer learning for scalability of neural-network quantum states
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• Artificial neural networks for density-functional optimizations in fermionic systems
• Density of states in an optical speckle potential
• Supervised machine learning of ultracold atoms with speckle disorder
• Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
• Few-boson localization in a continuum with speckle disorder

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