密度泛函理论（DFT）已成为材料界最有价值的计算工具之一。它指导了新型催化剂的发现、储能材料的设计、极端条件下材料行为的探索以及其他应用。DFT的成功在于其将量子力学中繁琐的多电子多核问题转化为有效的单电子Kohn-Sham（KS）方程。DFT的研究在理论、算法以及计算设施等方面均取得了巨大进展，在材料性质发现方面发挥了重大作用。然而，求解核心Kohn-Sham方程的计算成本仍然是大规模动力学研究复杂现象的主要障碍。在过去数十年内，各种基于机器学习（ML）的方法成为人们研究的热点，以满足DFT计算时遇到的长度和时间尺度需求。迄今，人们发展的方法能够在不同程度上成功预测电子结构或基本的原子性质，但还没有一套可靠的方案能够在一个综合的KS-DFT模拟中同时成功预测这两种属性。在本工作中，来自西班牙巴利亚多利德大学理论、原子和光学系的Beatriz G. del Rio等人，提出了一个端到端的ML模型，通过将系统的原子结构映射到它的电子电荷密度来模拟DFT的精髓，并通过使用原子结构和电荷密度作为输入来预测其他性质，如态密度、势能、原子受力和应力张量。这种策略与DFT的核心概念一致（电子电荷密度决定系统的所有特性），也与首次ML尝试（有了电子电荷密度就预测了各种特性）相一致，可以给出更准确、迁移性更高的结果。他们的深度学习模型成功避开了显式求解Kohn-Sham方程，在实现数量级加速的同时保持了化学精度。作者证实了这种ML-DFT思想适用于包含有机分子、聚合物链和聚合物晶体的大型数据库。该工作是向基于物理信息的DFT模拟器迈出的重要一步，能够成功、准确、同时再现Kohn-Sham方程的许多输出。
Editorial Summary
A deep learning framework to emulate DFT
Density functional theory (DFT) has become one of the most valuable computational tools for the materials research community. It has guided the discovery of new catalysts, the design of materials for energy storage, and the exploration of material behavior under extreme conditions, among other applications. The success of DFT lies in the transformation of the cumbersome many-electron many-nuclear problem of quantum mechanics to an effective one-electron Kohn–Sham (KS) equation. DFT-based research has seen several advancements in the areas of theory, algorithms, and computational infrastructure, instrumental in the above-mentioned discoveries. However, the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale. Over the last decade, machine learning (ML) based approaches are actively being considered in various ways to meet the length- and time-scale demands encountered during DFT computations. Although methods have been developed to varying degrees of success to predict either the electronic structure or basic atomic properties, there is yet no scheme that has successfully unified simultaneous prediction of both types of properties in a comprehensive KS-DFT emulation.In this work, Beatriz G. del Rio et al from the Departamento de Física Teórica, Atómica y Óptica of Universidad de Valladolid in Spain, proposed an end-to-end ML model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density, followed by the prediction of other properties such as density of states, potential energy, atomic forces, and stress tensor, by using the atomic structure and charge density as input. This strategy is consistent with the core concept underlying DFT (that the electronic charge density determines all properties of the system), and is aligned with the first rudimentary ML attempt in which a variety of properties were predicted given just the electronic charge density. In practice, this route also leads to more accurate and transferable results. The deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup, while maintaining chemical accuracy. They demonstrated the capability of this ML-DFT concept for an extensive database of organic molecules, polymer chains, and polymer crystals. This work represents an important step toward a physically-informed ML-based DFT emulator, which successfully, accurately, and simultaneously reproduces many of the outputs of the KS equation.
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