Molecular Potential Energy Computation via Graph Edge Aggregate Attention Neural Network

Jian Chang Yiming Kuai Xian Wei Hui Yu Hai Lan

Jian Chang, Yiming Kuai, Xian Wei, Hui Yu, Hai Lan. Molecular Potential Energy Computation via Graph Edge Aggregate Attention Neural Network[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2209136
Citation: Jian Chang, Yiming Kuai, Xian Wei, Hui Yu, Hai Lan. Molecular Potential Energy Computation via Graph Edge Aggregate Attention Neural Network[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2209136

doi: 10.1063/1674-0068/cjcp2209136

Molecular Potential Energy Computation via Graph Edge Aggregate Attention Neural Network

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  • Figure  1.  Framework of our model. MPNN is used as backbone (middle). The framework consists of feature embedding block (orange dotted box), EAA interaction block (blue dotted box), output block (green dotted box).

    Figure  2.  Schematic diagram of EAA.

    Figure  3.  Potential energy distribution of eight organic molecules in MD17 dataset.

    Figure  4.  The fitting errors for the malonaldehyde (upper), uracil (bottom) testing dataset with Schnet (left) and EAA (right). The horizontal axis denotes the distribution of ground truth energies of a given molecule dataset.

    Figure  5.  (a) Performance comparison of models with different head numbers. (b) Performance comparison of models with different layer numbers.

    Table  I.   Mean absolute errors for energy and force prediction ( in kcal/mol and kcal·mol−1· Å−1 ) for different training samples on MD17 dataset. GM-sNN [18], EANN [16], SchNet [33], PhysNet [35] results are compared. EANN does not provide results on Benzene molecule.The lowest error is emphasized in bold.

    Mean absolute error
    N = 1000N = 50000
    SchnetEANNGM-sNNEAASchnetPhysNetGM-sNNEAA
    Benzene Energy 0.08 0.08 ${\bf{0.06}}$ ${\bf{0.07}}$ ${\bf{0.07}}$ ${\bf{0.07}}$ 0.10
    Force 0.31 ${\bf{0.21}}$ 0.34 0.17 0.15 ${\bf{0.14}}$ 0.17
    Toluene Energy 0.12 ${\bf{0.11}}$ 0.15 ${\bf{0.11}}$ 0.09 0.10 0.14 ${\bf{0.07}}$
    Force 0.57 0.38 ${\bf{0.34}}$ 0.42 0.09 ${\bf{0.03}}$ 0.10 0.05
    Malonaldehyde Energy 0.13 0.14 0.12 ${\bf{0.10}}$ 0.08 ${\bf{0.07}}$ 0.12 ${\bf{0.07}}$
    Force 0.66 0.62 0.45 ${\bf{0.40}}$ 0.08 ${\bf{0.04}}$ 0.08 ${\bf{0.04}}$
    Salicylic acid Energy 0.20 ${\bf{0.14}}$ 0.19 0.16 0.10 0.11 0.19 ${\bf{ 0.09}}$
    Force 0.85 0.51 ${\bf{0.49}}$ 0.52 0.19 ${\bf{0.04}}$ 0.14 0.09
    Aspirin Energy 0.37 0.33 0.38 ${\bf{0.32}}$ 0.12 0.12 0.19 ${\bf{0.11}}$
    Force 1.35 0.99 ${\bf{0.69}}$ 0.99 0.33 ${\bf{0.06}}$ 0.26 0.14
    Ethanol Energy 0.08 0.10 0.10 ${\bf{0.07}}$ 0.05 0.05 0.05 ${\bf{0.04}}$
    Force 0.39 0.47 0.33 ${\bf{0.22}}$ 0.05 0.03 0.06 ${\bf{0.02}}$
    Uracil Energy 0.14 ${\bf{0.11}}$ 0.12 ${\bf{0.11}}$ ${\bf{0.10}}$ ${\bf{0.10}}$ ${\bf{0.10}}$ ${\bf{0.10}}$
    Force 0.56 0.35 ${\bf{0.33}}$ 0.36 0.11 ${\bf{0.03}}$ 0.07 0.04
    Naphthalene Energy 0.16 ${\bf{0.12}}$ 0.17 0.15 0.11 0.12 0.13 ${\bf{0.08}}$
    Force 0.58 ${\bf{0.27}}$ 0.36 0.36 0.11 ${\bf{0.04}}$ 0.13 0.05
    下载: 导出CSV

    Table  II.   Results with different training samples N. Scores are given by mean absolute errors of energy (kcal/mol) and force (kcal/(mol· Å)) prediction.

    DatasetNMean absolute error
    SchnetEAA
    EnergyForceEnergyForce
    Malonaldehyde 200 0.48 1.25 0.28 1.44
    400 0.27 0.92 0.18 0.89
    600 0.21 0.78 0.14 0.66
    800 0.17 0.71 0.12 0.52
    1000 0.13 0.66 0.10 0.40
    Uracil 200 0.40 1.45 0.20 1.12
    400 0.36 1.09 0.15 0.58
    600 0.28 0.89 0.13 0.50
    800 0.20 0.74 0.12 0.42
    1000 0.14 0.56 0.11 0.36
    下载: 导出CSV

    Table  III.   MAE results with different attention mechanisms. Scores are given by mean absolute errors of energy (kcal/mol) and force (kcal/mol/Å) prediction.

    Attention
    on node
    Attention
    on edge
    Malonaldehyde Uracil
    Energy Force Energy Force
    W/O W/O 0.13 0.66 0.14 0.56
    W W/O 0.14 0.49 0.12 0.44
    W W 0.10 0.44 0.11 0.36
    下载: 导出CSV

    Table  IV.   Mean absolute error per molecule of predictions for different target properties of the QM9 dataset using 110k training examples. The lowest error is emphasized in bold. Provably powerful graph networks (PPGN) [19], SchNet [33] and enn-s2s [24] results are compared.

    ParametersDescriptionUnitPPGNSchNetenn-s2sEAA
    ${\epsilon_{\rm{homo}} }$ Energy of highest occupied molecular orbital ${\rm{meV}}$ 40 41 43 ${\bf{33}}$
    ${\epsilon_{\rm{lumo}} }$ Energy of lowest unoccupied molecular orbital ${\rm{meV}}$ 33 34 37 ${\bf{27}}$
    ${\Delta\epsilon }$ Difference between LUMO and HOMO ${\rm{meV}}$ 60 63 69 ${\bf{54}}$
    ${\rm{ZPVE}}$ Dipole moment ${\rm{meV} }$ 3.12 1.7 ${\bf{1.5}}$ 1.6
    ${\mu}$ Dipole moment ${\rm{Debye}}$ 0.047 0.033 ${\bf{0.030}}$ 0.042
    ${\alpha}$ Isotropic polarizability ${\rm{Bohr}^3}$ 0.131 0.235 0.092 ${\bf{0.086}}$
    $\langle R^2 \rangle$ Electronic spatial extent ${\rm{Bohr}^2}$ 0.592 ${\bf{0.073}}$ 0.180 0.241
    ${U_0 }$ Internal energy at 0 K ${\rm{meV}}$ 37 14 19 ${\bf{12}}$
    ${U}$ Internal energy at 298.15 K ${\rm{meV}}$ 37 19 19 ${\bf{15}}$
    ${H}$ Enthalpy at 298.15 K ${\rm{meV}}$ 36 ${\bf{14}}$ 17 ${\bf{14}}$
    ${G}$ Free energy at 298.15 K ${\rm{meV}}$ 36 ${\bf{14}}$ 19 ${\bf{14}}$
    ${C_v}$ Heat capacity at 298.15 K ${\rm{cal\cdot mol^{-1}\cdot K^{-1}} }$ 0.055 0.033 0.040 ${\bf{0.030}}$
    下载: 导出CSV
  • [1] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). doi: 10.1103/PhysRev.140.A1133
    [2] R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985). doi: 10.1103/PhysRevLett.55.2471
    [3] F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985). doi: 10.1103/PhysRevB.31.5262
    [4] M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984). doi: 10.1103/PhysRevB.29.6443
    [5] A. D. MacKerell Jr., D. Bashford, M. Bellott, R. L. Dunbrack Jr, J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F. T. K. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, W. E. Reiher, B. Roux, M. Schlenkrich, J. C. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiórkiewicz-Kuczera, D. Yin, and M. Karplus, J. Phys. Chem. B 102, 3586 (1998). doi: 10.1021/jp973084f
    [6] A. C. Van Duin, S. Dasgupta, F. Lorant, and W. A. Goddard, J. Phys. Chem. A 105, 9396 (2001). doi: 10.1021/jp004368u
    [7] B. Jiang, J. Li, and H. Guo, J. Phys. Chem. Lett. 11, 5120 (2020). doi: 10.1021/acs.jpclett.0c00989
    [8] S. Manzhos and T. Carrington Jr., Chem. Rev. 121, 10187 (2020). doi: 10.1021/acs.chemrev.0c00665
    [9] P. L. Kang, C. Shang, and Z. P. Liu, Acc. Chem. Res. 53, 2119 (2020). doi: 10.1021/acs.accounts.0c00472
    [10] J. Behler and M. Parrinello, Phys. Rev. Lett. 98, 146401 (2007). doi: 10.1103/PhysRevLett.98.146401
    [11] B. Jiang and H. Guo, J. Chem. Phys. 139, 054112 (2013). doi: 10.1063/1.4817187
    [12] Z. Xie and J. M. Bowman, J. Chem. Theory Comput. 6, 26 (2010). doi: 10.1021/ct9004917
    [13] R. Chen, K. Shao, B. Fu, and D. H. Zhang, J. Chem. Phys. 152, 204307 (2020). doi: 10.1063/5.0010104
    [14] L. Xiaoxiao, C. Shang, L. Li, R. Chen, B. Fu, X. Xu, and D. Zhang, Nat. Commun. 13, 4427 (2022). doi: 10.1038/s41467-022-32191-6
    [15] J. Han, L. Zhang, R. Car, and E. Weinan, Commun. Comput. Phys. 23, 629 (2018). doi: 10.4208/cicp.OA-2017-0213
    [16] Y. Zhang, C. Hu, and B. Jiang, J. Phys. Chem. Lett. 10, 4962 (2019). doi: 10.1021/acs.jpclett.9b02037
    [17] S. Foiles, M. Baskes, and M. S. Daw, Phys. Rev. B 33, 7983 (1986). doi: 10.1103/PhysRevB.33.7983
    [18] V. Zaverkin and J. Kästner, J. Chem. Theory Comput. 16, 5410 (2020). doi: 10.1021/acs.jctc.0c00347
    [19] H. Maron, H. Ben-Hamu, H. Serviansky, and Y. Lipman, in Advances in Neural Information Processing Systems 32, Vancouver, BC, Canada ((2019)).
    [20] K. Liu, X. Sun, L. Jia, J. Ma, H. Xing, J. Wu, H. Gao, Y. Sun, F. Boulnois, and J. Fan, Int. J. Mol. Sci. 20, 3389 (2019). doi: 10.3390/ijms20143389
    [21] W. Jin, R. Barzilay, and T. Jaakkola, Inernational Conference on Machine Learning, PMLR, 2323–2332 (2018).
    [22] T. Nguyen, H. Le, T. P. Quinn, T. Nguyen, T. D. Le, and S. Venkatesh, Bioinformatics 37, 1140 (2021). doi: 10.1093/bioinformatics/btaa921
    [23] K. T. Schütt, F. Arbabzadah, S. Chmiela, K. R. Müller, and A. Tkatchenko, Nat. Commun. 8, 1 (2017). doi: 10.1038/s41467-016-0009-6
    [24] W. Jin, R. Barzilay, and T. Jaakkola, in Proceedings of the 35th International Conference on Machine Learning, Long Beach, California, USA, (2018).
    [25] K. Schütt, O. Unke, and M. Gastegger, Internation Conference on Machine Learning, PMLR, 9377–9388 (2021).
    [26] Y. Zhang, J. Xia, and B. Jiang, J. Chem. Phys. 156, 114801 (2022). doi: 10.1063/5.0080766
    [27] O. T. Unke, S. Chmiela, M. Gastegger, K. T. Schütt, H. E. Sauceda, and K. R. Müller, Nat. Commun. 12, 1 (2021). doi: 10.1038/s41467-020-20314-w
    [28] P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio, International Conference on Learning Representations, (2018).
    [29] Z. Xiong, D. Wang, X. Liu, F. Zhong, X. Wan, X. Li, Z. Li, X. Luo, K. Chen, H. Jiang, and M. Zheng, J. Med. Chem. 63, 8749 (2020). doi: 10.1021/acs.jmedchem.9b00959
    [30] C. W. Coley, W. Jin, L. Rogers, T. F. Jamison, T. S. Jaakkola, W. H. Green, R. Barzilay, and K. F. Jensen, Chem. Sci. 10, 370 (2019). doi: 10.1039/C8SC04228D
    [31] A. Y. T. Wang, S. K. Kauwe, R. J. Murdock, and T. D. Sparks, Npj Comput. Mater. 7, 1 (2021). doi: 10.1038/s41524-020-00473-6
    [32] S. Y. Louis, Y. Zhao, A. Nasiri, X. Wang, Y. Song, F. Liu, and J. Hu, Phys. Chem. Chem. Phys. 22, 18141 (2020). doi: 10.1039/D0CP01474E
    [33] K. Schütt, P. J. Kindermans, H. E. Sauceda Felix, S. Chmiela, A. Tkatchenko, and K. R. Müller, in Advances in Neural Information Processing Systems 30, Long Beach, CA, USA ((2017)).
    [34] K. T. Schütt, H. E. Sauceda, P -J. Kindermans, A. Tkatchenko, and K. R. Müller, J. Chem. Phys. 148, 241722 (2018). doi: 10.1063/1.5019779
    [35] O. T. Unke and M. Meuwly, J. Chem. Theory Comput. 15, 3678 (2019). doi: 10.1021/acs.jctc.9b00181
    [36] D. P. Kingma and J. Ba, in 3rd International Conference on Learning Representations, San Diego, CA, USA, (2015).
    [37] I. Loshchilov and F. Hutter, in 5th International Conference on Learning Representations, Toulon, France, (2017).
    [38] S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. T. Schütt, and K. R. Müller, Sci. Adv 3, e1603015 (2017). doi: 10.1126/sciadv.1603015
    [39] R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. Von Lilienfeld, Sci. Data 1, 1 (2014). doi: 10.1038/sdata.2014.22
    [40] L. Ruddigkeit, R. Van Deursen, L. C. Blum, and J. L. Reymond, J. Chem. Inf. Model. 52, 2864 (2012). doi: 10.1021/ci300415d
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出版历程
  • 收稿日期:  2022-09-16
  • 录用日期:  2022-12-06
  • 网络出版日期:  2022-12-13

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