基于求解密度泛函理論（DFT）Kohn-Sham（KS）方程的模擬，已成為現(xiàn)代材料學(xué)和化學(xué)研究和開發(fā)組合過程的重要組成部分。盡管KS方程具有很強(qiáng)的普適性，但由于求解計(jì)算量很大，常規(guī)DFT計(jì)算一般只限于幾百個(gè)原子。

來自佐治亞理工學(xué)院的RampiRamprasad領(lǐng)導(dǎo)的團(tuán)隊(duì)，報(bào)道了一種基于機(jī)器學(xué)習(xí)的方法，可以不直接求解KS方程而有效預(yù)測(cè)電子結(jié)構(gòu)。該方法利用新的旋轉(zhuǎn)不變表示，將格點(diǎn)周圍的原子環(huán)境映射到該格點(diǎn)處的電子密度和局部態(tài)密度，并使用預(yù)先計(jì)算得到的帶有幾百萬的格點(diǎn)信息的DFT結(jié)果來訓(xùn)練的神經(jīng)網(wǎng)絡(luò)來獲得該映射。上述方法可以精確模擬實(shí)際求解KS方程的結(jié)果，但是速度快幾個(gè)數(shù)量級(jí)。此外，由于該方法的計(jì)算量與系統(tǒng)尺寸嚴(yán)格成線性關(guān)系，因而有望用于大型體系的電子結(jié)構(gòu)預(yù)測(cè)。

該文近期發(fā)表于Computational Materials5:22(2019)

Solving the electronic structure problem with machine learning

Anand Chandrasekaran, Deepak Kamal, Rohit Batra, Chiho Kim, Lihua Chen & Rampi Ramprasad

Simulations based on solving the Kohn-Sham (KS) equation of density functional theory (DFT) have become a vital component of modern materials and chemical sciences research and development portfolios. Despite its versatility, routine DFT calculations are usually limited to a few hundred atoms due to the computational bottleneck posed by the KS equation. Here we introduce a machine-learning-based scheme to efficiently assimilate the function of the KS equation, and by-pass it to directly, rapidly, and accurately predict the electronic structure of a material or a molecule, given just its atomic configuration. A new rotationally invariant representation is utilized to map the atomic environment around a grid-point to the electron density and local density of states at that grid-point. This mapping is learned using a neural network trained on previously generated reference DFT results at millions of grid-points. The proposed paradigm allows for the high-fidelity emulation of KS DFT, but orders of magnitude faster than the direct solution. Moreover, the machine learning prediction scheme is strictly linear-scaling with system size.