用机器学习加速硅的温度依赖能隙计算，仅需百次量子计算训练即可大幅提高采样效率。
Machine learning approach for vibronically renormalized electronic band structures
- 基于深度神经网络预测声子构型下的物理性质，跳过耗时的从头算计算。
- 仅需不到100次DFT计算训练，采样量提升一个数量级。
- 适用于需要高效处理温度效应的第一性原理电子结构研究者。
我们提出一种机器学习方法，用于高效计算基于第一性原理的物理性质在有限温度下的振动热期望值。该方法基于非微扰冻结声子框架，利用随机蒙特卡洛算法根据第一性原理声子模型，在超胞中采样有限温度下的原子核构型。通过深度神经网络对采样构型对应的物理性质进行准确预测，从而避免耗时的从头算计算。为将电子系统的点群对称性融入机器学习模型，采用群论方法构建了超胞声子构型的对称性不变描述符。我们将该方法应用于基于密度泛函理论（DFT）的硅的温度依赖电子能隙计算。结果表明，仅需不到100次DFT计算用于训练神经网络模型，即可实现比传统方法高一个数量级的采样规模，显著提升了振动热期望值的计算效率。本工作展示了机器学习技术在有限温度第一性原理电子结构方法中的巨大潜力。
原文摘要 · Abstract (English)
We present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the non-perturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming {\em ab initio} calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.
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