Solving the electronic structure problem with machine learning
Source abstract
Abstract
Abstract Simulations 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.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Machine Learning in Materials Science · X-ray Diffraction in Crystallography · Advanced Chemical Physics Studies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (44)
Show source-provided references
1. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436 (2015).10.1038/nature14539 ↗
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).
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
10. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).10.1103/PhysRev.136.B864 ↗
11. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).10.1103/PhysRev.140.A1133 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
19. Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 134, 074106 (2011).10.1063/1.3553717 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
29. Sharma, V. et al. Rational design of all organic polymer dielectrics. Nat. Commun. 5, 4845 (2014).10.1038/ncomms5845 ↗
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 ↗
31. Xue, D. et al. Accelerated search for materials with targeted properties by adaptive design. Nat. Commun. 7, 1–9 (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 ↗
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 ↗
34. Pilania, G. et al. Machine learning bandgaps of double perovskites. Sci. Rep. 6, 19375 (2016).10.1038/srep19375 ↗
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 ↗
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 ↗
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 ↗
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 ↗
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 ↗
40. Brockherde, F. et al. Bypassing the kohn-sham equations with machine learning. Nat. Commun. 8, 872 (2017).10.1038/s41467-017-00839-3 ↗
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 ↗
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 ↗
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 ↗