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Artificial neural networks for density-functional optimizations in fermionic systems.

Caio A Custódio1, Érica R Filletti1, Vivian V França2

  • 1Institute of Chemistry, São Paulo State University, UNESP, 14800-090, Araraquara, São Paulo, Brazil.

Scientific Reports
|February 15, 2019
PubMed
Summary
This summary is machine-generated.

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We developed a novel artificial neural network functional for calculating the ground-state energy of interacting fermionic particles. This neural network functional achieves high accuracy, outperforming analytical methods and reducing computational cost.

Area of Science:

  • Condensed Matter Physics
  • Computational Physics
  • Quantum Chemistry

Background:

  • The Hubbard model is a fundamental model for understanding strongly correlated electron systems.
  • Accurate calculation of ground-state energy is crucial for predicting material properties.
  • Existing analytical functionals often struggle with accuracy, especially in weakly interacting regimes.

Purpose of the Study:

  • To develop and validate a novel artificial neural network functional for the ground-state energy of fermionic particles.
  • To assess the performance of the neural network functional against numerically exact calculations and analytical methods.
  • To evaluate the applicability of the developed functional to various system types, including finite and confined systems.

Main Methods:

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  • Development of an artificial neural network (ANN) functional tailored for the Hubbard model.
  • Comparison of ANN functional predictions with numerically exact solutions for homogeneous fermionic chains.
  • Application of the ANN functional to finite systems with impurities and harmonic confinement within density-functional theory (DFT).

    • Main Results:

    • The ANN functional demonstrated excellent accuracy, with deviations less than 0.15% from exact calculations across various interaction, filling, and magnetization regimes.
    • The neural functional significantly outperformed analytical functionals, particularly in the weakly interacting regime (0.1% vs. 7% error).
    • The ANN approach achieved accuracy comparable to more computationally expensive DFT and many-body methods, but at a fraction of the cost.

    Conclusions:

    • Artificial neural network functionals offer a highly accurate and computationally efficient alternative for calculating ground-state energies in fermionic systems.
    • The developed ANN functional shows great promise for advancing the accuracy and efficiency of electronic structure calculations in condensed matter physics and quantum chemistry.
    • This work paves the way for more sophisticated machine learning applications in materials science and quantum simulations.