Solving the electronic structure problem with machine learning
10.1038/s41524-019-0162-7
Crossref journal-article
Springer Science and Business Media LLC
npj Computational Materials (297)
Abstract

AbstractSimulations 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.

Bibliography

Chandrasekaran, A., Kamal, D., Batra, R., Kim, C., Chen, L., & Ramprasad, R. (2019). Solving the electronic structure problem with machine learning. Npj Computational Materials, 5(1).

Authors 6
  1. Anand Chandrasekaran (first)
  2. Deepak Kamal (additional)
  3. Rohit Batra (additional)
  4. Chiho Kim (additional)
  5. Lihua Chen (additional)
  6. Rampi Ramprasad (additional)
References 44 Referenced 255
  1. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436 (2015). (10.1038/nature14539) / Nature by Y LeCun (2015)
  2. Geiger, A., Lenz, P. & Urtasun, R. Are we ready for autonomous driving? The KITTI vision benchmark suite. In 2012 IEEE Conference on Computer Vision and Pattern Recognition, IEEE, Piscataway, NJ, USA, 3354–3361 (2012). (10.1109/CVPR.2012.6248074)
  3. Mueller, T., Kusne, A. G. & Ramprasad, R. Machine learning in materials science: recent progress and emerging applications. Rev. Comp. Ch. 29, 186–273 (2016). / Rev. Comp. Ch. by T Mueller (2016)
  4. Huo, H. & Rupp, M. Unified representation for machine learning of molecules and crystals. Preprint (2017) https://arxiv.org/abs/1704.06439.
  5. Bartók, A. P., Payne, M. C., Kondor, R. & Csányi, G. Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010). (10.1103/PhysRevLett.104.136403) / Phys. Rev. Lett. by AP Bartók (2010)
  6. Rupp, M., Tkatchenko, A., Müller, K.-R. & Von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 108, 058301 (2012). (10.1103/PhysRevLett.108.058301) / Phys. Rev. Lett. by M Rupp (2012)
  7. Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007). (10.1103/PhysRevLett.98.146401) / Phys. Rev. Lett. by J Behler (2007)
  8. Botu, V. & Ramprasad, R. Learning scheme to predict atomic forces and accelerate materials simulations. Phys. Rev. B 92, 094306 (2015). (10.1103/PhysRevB.92.094306) / Phys. Rev. B by V Botu (2015)
  9. von Lilienfeld, O. A., Ramakrishnan, R., Rupp, M. & Knoll, A. Fourier series of atomic radial distribution functions: a molecular fingerprint for machine learning models of quantum chemical properties. Int. J. Quantum Chem. 115, 1084–1093 (2015). (10.1002/qua.24912) / Int. J. Quantum Chem. by OA von Lilienfeld (2015)
  10. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964). (10.1103/PhysRev.136.B864) / Phys. Rev. by P Hohenberg (1964)
  11. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965). (10.1103/PhysRev.140.A1133) / Phys. Rev. by W Kohn (1965)
  12. Ramprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A. & Kim, C. Machine learning in materials informatics: recent applications and prospects. npj Comput. Mater. 3, 54 (2017). (10.1038/s41524-017-0056-5) / npj Comput. Mater. by R Ramprasad (2017)
  13. Jain, A., Shin, Y. & Persson, K. A. Computational predictions of energy materials using density functional theory. Nat. Rev. Mater. 1, 15004 (2016). (10.1038/natrevmats.2015.4) / Nat. Rev. Mater. by A Jain (2016)
  14. Mannodi-Kanakkithodi, A. et al. Rational co-design of polymer dielectrics for energy storage. Adv. Mater. 28, 6277–6291 (2016). (10.1002/adma.201600377) / Adv. Mater. by A Mannodi-Kanakkithodi (2016)
  15. Mannodi-Kanakkithodi, A. et al. Scoping the polymer genome: a roadmap for rational polymer dielectrics design and beyond. Mater. Today 21, 785–796 (2018). (10.1016/j.mattod.2017.11.021) / Mater. Today by A Mannodi-Kanakkithodi (2018)
  16. Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246 (2018). (10.1038/s41565-017-0035-5) / Nat. Nanotechnol. by N Mounet (2018)
  17. Tabor, D. P. et al. Accelerating the discovery of materials for clean energy in the era of smart automation. Nat. Rev. Mater. 3, 5–20 (2018). (10.1038/s41578-018-0005-z) / Nat. Rev. Mater. by DP Tabor (2018)
  18. Botu, V. & Ramprasad, R. Adaptive machine learning framework to accelerate ab initio molecular dynamics. Int. J. Quantum Chem. 115, 1074–1083 (2015). (10.1002/qua.24836) / Int. J. Quantum Chem. by V Botu (2015)
  19. Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 134, 074106 (2011). (10.1063/1.3553717) / J. Chem. Phys. by J Behler (2011)
  20. Schütt, K. et al. Schnet: a continuous-filter convolutional neural network for modeling quantum interactions. In Advances in Neural Information Processing Systems 30 (eds Guyon, I. et al.) 991–1001 (Curran Associates, Inc., 2017). http://papers.nips.cc/paper/6700-schnet-a-continuous-filter-convolutional-neural-network-for-modeling-quantum-interactions.pdf.
  21. Botu, V., Batra, R., Chapman, J. & Ramprasad, R. Machine learning force fields: construction, validation, and outlook. J. Phys. Chem. C 121, 511–522 (2017). (10.1021/acs.jpcc.6b10908) / J. Phys. Chem. C by V Botu (2017)
  22. Kolb, B., Lentz, L. C. & Kolpak, A. M. Discovering charge density functionals and structure-property relationships with prophet: a general framework for coupling machine learning and first-principles methods. Sci. Rep. 7, 1192 (2017). (10.1038/s41598-017-01251-z) / Sci. Rep. by B Kolb (2017)
  23. Huan, T. D. et al. A universal strategy for the creation of machine learning-based atomistic force fields. npj Comput. Mater. 3, 37 (2017). (10.1038/s41524-017-0042-y) / npj Comput. Mater. by TD Huan (2017)
  24. Smith, J. S., Isayev, O. & Roitberg, A. E. Ani-1: an extensible neural network potential with dft accuracy at force field computational cost. Chem. Sci. 8, 3192–3203 (2017). (10.1039/C6SC05720A) / Chem. Sci. by JS Smith (2017)
  25. Imbalzano, G. et al. Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials. J. Chem. Phys. 148, 241730 (2018). (10.1063/1.5024611) / J. Chem. Phys. by G Imbalzano (2018)
  26. Bianchini, F., Kermode, J. R. & Vita, A. D. Modelling defects in Ni–Al with eam and dft calculations. Model. Simul. Mater. Sci. Eng. 24, 045012 (2016). (10.1088/0965-0393/24/4/045012) / Model. Simul. Mater. Sci. Eng. by F Bianchini (2016)
  27. Khaliullin, R. Z., Eshet, H., Kühne, T. D., Behler, J. & Parrinello, M. Nucleation mechanism for the direct graphite-to-diamond phase transition. Nat. Mat. 10, 693 (2011). (10.1038/nmat3078) / Nat. Mat. by RZ Khaliullin (2011)
  28. Meredig, B. et al. Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys. Rev. B 89, 094104 (2014). (10.1103/PhysRevB.89.094104) / Phys. Rev. B by B Meredig (2014)
  29. Sharma, V. et al. Rational design of all organic polymer dielectrics. Nat. Commun. 5, 4845 (2014). (10.1038/ncomms5845) / Nat. Commun. by V Sharma (2014)
  30. Kim, C., Pilania, G. & Ramprasad, R. Machine learning assisted predictions of intrinsic dielectric breakdown strength of abx3 perovskites. J. Phys. Chem. C 120, 14575–14580 (2016). (10.1021/acs.jpcc.6b05068) / J. Phys. Chem. C by C Kim (2016)
  31. Xue, D. et al. Accelerated search for materials with targeted properties by adaptive design. Nat. Commun. 7, 1–9 (2016). / Nat. Commun. by D Xue (2016)
  32. Huan, T. D. et al. A polymer dataset for accelerated property prediction and design. Sci. Data 3, 160012 (2016). (10.1038/sdata.2016.12) / Sci. Data by TD Huan (2016)
  33. Mannodi-Kanakkithodi, A., Pilania, G., Huan, T. D., Lookman, T. & Ramprasad, R. Machine learning strategy for accelerated design of polymer dielectrics. Sci. Rep. 6, 20952 (2016). (10.1038/srep20952) / Sci. Rep. by A Mannodi-Kanakkithodi (2016)
  34. Pilania, G. et al. Machine learning bandgaps of double perovskites. Sci. Rep. 6, 19375 (2016). (10.1038/srep19375) / Sci. Rep. by G Pilania (2016)
  35. Balachandran, P. V. et al. Predictions of new ABO3 perovskite compounds by combining machine learning and density functional theory. Phys. Rev. Mater. 2, 043802 (2018). (10.1103/PhysRevMaterials.2.043802) / Phys. Rev. Mater. by PV Balachandran (2018)
  36. Sanchez-Lengeling, B. & Aspuru-Guzik, A. Inverse molecular design using machine learning: generative models for matter engineering. Science 361, 360–365 (2018). (10.1126/science.aat2663) / Science by B Sanchez-Lengeling (2018)
  37. Snyder, J. C., Rupp, M., Hansen, K., Müller, K.-R. & Burke, K. Finding density functionals with machine learning. Phys. Rev. Lett. 108, 253002 (2012). (10.1103/PhysRevLett.108.253002) / Phys. Rev. Lett. by JC Snyder (2012)
  38. Montavon, G. et al. Machine learning of molecular electronic properties in chemical compound space. New J. Phys. 15, 1305.7074 (2013). (10.1088/1367-2630/15/9/095003) / New J. Phys. by G Montavon (2013)
  39. Schütt, K. T. et al. How to represent crystal structures for machine learning: towards fast prediction of electronic properties. Phys. Rev. B 89, 205118 (2014). (10.1103/PhysRevB.89.205118) / Phys. Rev. B by KT Schütt (2014)
  40. Brockherde, F. et al. Bypassing the kohn-sham equations with machine learning. Nat. Commun. 8, 872 (2017). (10.1038/s41467-017-00839-3) / Nat. Commun. by F Brockherde (2017)
  41. Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & Müller, K.-R. Schnet–a deep learning architecture for molecules and materials. J. Chem. Phys. 148, 241722 (2018). (10.1063/1.5019779) / J. Chem. Phys. by KT Schütt (2018)
  42. Graves, A., Mohamed, A. & Hinton, G. Speech recognition with deep recurrent neural networks. In 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE, Piscataway, NJ, USA, 6645–6649 (2013). (10.1109/ICASSP.2013.6638947)
  43. Ruddigkeit, L., van Deursen, R., Blum, L. C. & Reymond, J.-L. Enumeration of 166 billion organic small molecules in the chemical universe database gdb-17. J. Chem. Inf. Model. 52, 2864–2875 (2012). (10.1021/ci300415d) / J. Chem. Inf. Model. by L Ruddigkeit (2012)
  44. Ramakrishnan, R., Dral, P. O., Rupp, M. & Von Lilienfeld, O. A. Quantum chemistry structures and properties of 134 kilo molecules. Sci. Data 1, 140022 (2014). (10.1038/sdata.2014.22) / Sci. Data by R Ramakrishnan (2014)
Dates
Type When
Created 6 years, 6 months ago (Feb. 18, 2019, 6:03 a.m.)
Deposited 2 years, 8 months ago (Dec. 16, 2022, 9:42 p.m.)
Indexed 1 day, 15 hours ago (Aug. 29, 2025, 6:01 a.m.)
Issued 6 years, 6 months ago (Feb. 18, 2019)
Published 6 years, 6 months ago (Feb. 18, 2019)
Published Online 6 years, 6 months ago (Feb. 18, 2019)
Funders 1
  1. United States Department of Defense | United States Navy | Office of Naval Research 10.13039/100000006 Office of Naval Research

    Region: Americas

    gov (National government)

    Labels6
    1. U.S. Office of Naval Research
    2. Naval Research
    3. United States Office of Naval Research
    4. U.S. Department of the Navy Office of Naval Research
    5. The Office of Naval Research
    6. ONR
    Awards1
    1. N0014- 17-1-2656

@article{Chandrasekaran_2019, title={Solving the electronic structure problem with machine learning}, volume={5}, ISSN={2057-3960}, url={http://dx.doi.org/10.1038/s41524-019-0162-7}, DOI={10.1038/s41524-019-0162-7}, number={1}, journal={npj Computational Materials}, publisher={Springer Science and Business Media LLC}, author={Chandrasekaran, Anand and Kamal, Deepak and Batra, Rohit and Kim, Chiho and Chen, Lihua and Ramprasad, Rampi}, year={2019}, month=feb }