Institute of Chemistry, São Paulo State University, UNESP, 14800-090, Araraquara, São Paulo, Brazil.
Sci Rep. 2019 Feb 13;9(1):1886. doi: 10.1038/s41598-018-37999-1.
In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to have an excellent performance: it deviates from numerically exact calculations by less than 0.15% for a vast regime of interactions and for all the regimes of filling factors and magnetizations. When compared to analytical functionals, the neural functional was found to be more precise for all the regimes of parameters, being particularly superior at the weakly interacting regime: where the analytical parametrization fails the most, ~7%, against only ~0.1% for the neural network. We have also applied our homogeneous functional to finite, localized impurities and harmonically confined systems within density-functional theory (DFT) methods. The results show that while our artificial neural network approach is substantially more accurate than other equivalently simple and fast DFT treatments, it has similar performance than more costly DFT calculations and other independent many-body calculations, at a fraction of the computational cost.
在这项工作中，我们提出了一个人工神经网络，用于描述由 Hubbard 模型描述的均匀链中相互作用费米子的基态能量。我们的神经网络函数被证明具有出色的性能：对于广泛的相互作用范围以及所有填充因子和磁化率范围，它与数值精确计算的偏差小于 0.15%。与解析泛函相比，神经网络泛函在所有参数范围内都更加精确，在弱相互作用范围内尤其优越：在那里，解析参数化最失败，约为 7%，而神经网络仅为约 0.1%。我们还将我们的均匀泛函应用于有限的、局部的杂质和谐波约束系统，采用密度泛函理论（DFT）方法。结果表明，虽然我们的人工神经网络方法比其他同样简单和快速的 DFT 处理方法准确得多，但它与更昂贵的 DFT 计算和其他独立的多体计算具有相似的性能，计算成本仅为其一小部分。
