Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. The central challenge is how to encode a highly-complex quantum-many-body wave function compactly. Here, we demonstrate that artificial neural networks, known for their overwhelming expressibility in the context of machine learning, are excellent tool for first-principles calculations of extended periodic materials. We show that the ground-state energies in real solids in one-, two-, and three-dimensional systems are simulated precisely, reaching their chemical accuracy. The highlight of our work is that the quasiparticle band spectra, which are both essential and peculiar to solid-state systems, can be efficiently extracted with a computational technique designed to exploit the low-lying energy structure from neural networks. This work opens up a path to elucidate the intriguing and complex many-body phenomena in solid-state systems.

建立固体系统的预测性从头计算方法是凝聚态物理和计算材料科学的基本目标之一。中心挑战是如何紧凑地编码高度复杂的量子多体波函数。在这里，我们证明了人工神经网络，以其在机器学习中的压倒性的可表达性而闻名，是扩展周期材料的第一性原理计算的出色工具。我们表明，在一维，二维和三维系统中，真实固体中的基态能量得到了精确模拟，达到了化学精度。我们工作的重点是准粒子能谱，这对于固态系统来说是必不可少的，可以使用旨在利用神经网络的低层能量结构的计算技术来有效地提取能量。这项工作为阐明固态系统中有趣而复杂的多体现象开辟了道路。