Here we listed some DFA-inspired NN.
[1]PauliNet: Pfau, D.; Spencer, J. S.; Matthews, A. G.; Foulkes, W. M. C., Ab initio solution of the many-electron Schrödinger equation with deep neural networks. Phy. Rev. Res. 2020, 2 (3), 033429.
[2]FermiNet: Hermann, J.; Schätzle, Z.; Noé, F., Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 2020, 12 (10), 891-897.
[3]QDF: Tsubaki, M.; Mizoguchi, T., Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning. Phys. Rev. Lett. 2020, 125 (20), 206401.
[4]GOODLE: Lin, H.; Ye, S.; Zhu, X., Geometry Orbital of Deep Learning (GOODLE): A uniform carbon potential. Carbon 2022, 186, 313-319.
[5]OrbNet: Qiao, Z.; Welborn, M.; Anandkumar, A.; Manby, F. R.; Miller III, T. F., OrbNet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital features. J. chem. phys. 2020, 153 (12), 124111.
[6]AIMNet: Zubatyuk, R.; Smith, J. S.; Leszczynski, J.; Isayev, O., Accurate and transferable multitask prediction of chemical properties with an atoms-in-molecules neural network. Sci. adv. 2019, 5 (8), eaav6490.
[7]TorchANI: Gao, X.; Ramezanghorbani, F.; Isayev, O.; Smith, J. S.; Roitberg, A. E., TorchANI: a free and open source PyTorch-based deep learning implementation of the ANI neural network potentials. J. chem. infor. model 2020, 60 (7), 3408-3415.
[8]Brockherde, F., Vogt, L., Li, L., Tuckerman, M. E., Burke, K., & Müller, K. R. (2017). Bypassing the Kohn-Sham equations with machine learning. Nat. comm., 8(1), 1-10.
[9]ANI-1: Smith, J. S., Isayev, O., & Roitberg, A. E. (2017). ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. sci. 8(4), 3192-3203.
[10]SchNOrb: Westermayr, J., Gastegger, M., & Marquetand, P. (2020). Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamics. J. phys. chem. lett., 11(10), 3828-3834.
[11]TensorMol: Yao, K., Herr, J. E., Toth, D. W., Mckintyre, R., & Parkhill, J. (2018). The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics. Chem. sci., 9(8), 2261-2269.