Transferable machine-learning model of the electron density. Bypassing the Kohn-Sham equations with machine learning. SpookyNet: learning force fields with electronic degrees of freedom and nonlocal effects. International Conference on Learning Representations (ICLR, 2020) Directional message passing for molecular graphs. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Schnet-a deep learning architecture for molecules and materials. Generalized neural-network representation of high-dimensional potential-energy surfaces. Machine learning and the physical sciences. Machine learning: trends, perspectives and prospects. Density functional theory: its origins, rise to prominence and future. Self-consistent equations including exchange and correlation effects. The method provides a solution to the accuracy–efficiency dilemma of DFT and opens opportunities to explore large-scale material systems, as evidenced by a promising application in the study of twisted van der Waals materials. High accuracy, high efficiency and good transferability of the DeepH method are generally demonstrated for various kinds of material system and physical property. A general framework is proposed to deal with the large dimensionality and gauge (or rotation) covariance of the DFT Hamiltonian matrix by virtue of locality, and this is realized by a message-passing neural network for deep learning. Here we develop a deep neural network approach to represent the DFT Hamiltonian (DeepH) of crystalline materials, aiming to bypass the computationally demanding self-consistent field iterations of DFT and substantially improve the efficiency of ab initio electronic-structure calculations. The marriage of density functional theory (DFT) and deep-learning methods has the potential to revolutionize modern computational materials science.
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