Learning from data has led to paradigm shifts in a multitude of disciplines,
including web, text, and image search, speech recognition, as well as
bioinformatics. Can machine learning enable similar breakthroughs in
understanding quantum many-body systems? Here we develop an efficient deep
learning approach that enables spatially and chemically resolved insights into
quantum-mechanical observables of molecular systems. We unify concepts from
many-body Hamiltonians with purpose-designed deep tensor neural networks
(DTNN), which leads to size-extensive and uniformly accurate (1 kcal/mol)
predictions in compositional and configurational chemical space for molecules
of intermediate size. As an example of chemical relevance, the DTNN model
reveals a classification of aromatic rings with respect to their stability -- a
useful property that is not contained as such in the training dataset. Further
applications of DTNN for predicting atomic energies and local chemical
potentials in molecules, reliable isomer energies, and molecules with peculiar
electronic structure demonstrate the high potential of machine learning for
revealing novel insights into complex quantum-chemical systems.

本文提出了一种基于深度张量神经网络（DTNN）的方法，可以实现空间和化学分辨率高的分子系统在量子力学观测量方面的分析，此方法可以用于预测分子的原子能和局部化学势，同位素能和分子的电子结构，为揭示复杂的量子化学体系提供了新的突破。