Orbital-free density functional theory (OF-DFT) holds the promise to compute
ground state molecular properties at minimal cost. However, it has been held
back by our inability to compute the kinetic energy as a functional of the
electron density only. We here set out to learn the kinetic energy functional
from ground truth provided by the more expensive Kohn-Sham density functional
theory. Such learning is confronted with two key challenges: Giving the model
sufficient expressivity and spatial context while limiting the memory footprint
to afford computations on a GPU; and creating a sufficiently broad distribution
of training data to enable iterative density optimization even when starting
from a poor initial guess. In response, we introduce KineticNet, an equivariant
deep neural network architecture based on point convolutions adapted to the
prediction of quantities on molecular quadrature grids. Important contributions
include convolution filters with sufficient spatial resolution in the vicinity
of the nuclear cusp, an atom-centric sparse but expressive architecture that
relays information across multiple bond lengths; and a new strategy to generate
varied training data by finding ground state densities in the face of
perturbations by a random external potential. KineticNet achieves, for the
first time, chemical accuracy of the learned functionals across input densities
and geometries of tiny molecules. For two electron systems, we additionally
demonstrate OF-DFT density optimization with chemical accuracy.

使用 KineticNet 深度神经网络对轨道自由密度泛函理论中的动能能量进行建模，通过分子平面网格预测分子的动能能量函数，以获得具有化学准确性的模型，从而实现轨道自由密度泛函理论的密度优化，以及对小分子的基态分子属性计算。

KineticNet: 深度学习转移动能能量泛函应用于无轨道密度泛函理论

KineticNet: Deep learning a transferable kinetic energy functional for  orbital-free density functional theory

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of
density functional theory to solve electronic structure problems in a wide
variety of scientific fields, ranging from materials science to biochemistry to
astrophysics. Machine learning holds the promise of learning the kinetic energy
functional via examples, by-passing the need to solve the Kohn-Sham equations.
This should yield substantial savings in computer time, allowing either larger
systems or longer time-scales to be tackled, but attempts to machine-learn this
functional have been limited by the need to find its derivative. The present
work overcomes this difficulty by directly learning the density-potential and
energy-density maps for test systems and various molecules. Both improved
accuracy and lower computational cost with this method are demonstrated by
reproducing DFT energies for a range of molecular geometries generated during
molecular dynamics simulations. Moreover, the methodology could be applied
directly to quantum chemical calculations, allowing construction of density
functionals of quantum-chemical accuracy.

本文介绍一种基于机器学习的方法，通过学习电子结构问题的动能泛函，直接学习测试系统和各种分子的密度势和能量密度图，并演示了该方法通过复制分子动力学模拟期间生成的一系列分子几何体系，实现了改进的精度和较低的计算成本，同时还探讨了该方法可直接应用于量子化学计算，以构建量子化学精度的密度泛函。