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## Machine Learning Density Functional Theory

Our group was the first to apply robust machine learning (ML) methods to directly 'learn' density functionals. ML is a powerful method capable of learning functions of high-dimensional spaces via induction.

Most DFT research solving the kinetic energy from Kohn-Sham equation. However, it is not needed in principle from the theorems of DFT. If the kinetic energy of such electrons were known as a functional of density, then a single equation could be solved for the exact self-consistent density and the energy extracted. There would be no need to solve the KS equations, and the computational bottleneck would presumably become solving the Poisson equation. Thus DFT calculations would become much faster than they already are.

In a proof-of-principle [Phys. Rev. Lett. 108, 253002 (2012)], we used ML to approximate the kinetic energy functional of particles confined to a one-dimensional box with chemical accuracy. We are actively researching extending this method to 3d systems. Applying this method to real complex systems would enable highly accurate orbital-free density functional calculations and ab-initio molecular dynamics simulations.

###### Publications

[184] | Can exact conditions improve machine-learned density functionals? Jacob Hollingsworth, Li Li, Thomas E. Baker, Kieron Burke, The Journal of Chemical Physics 148, 241743 (2018).
[bibtex] [pdf] |

[175] | Pure density functional for strong correlation and the thermodynamic limit from machine learning Li Li, Thomas E. Baker, Steven R. White, Kieron Burke, Phys. Rev. B 94, 245129 (2016).
[bibtex] [pdf] |

[174] | By-passing the Kohn-Sham equations with machine learning Felix Brockherde, Leslie Vogt, Li Li, Mark E Tuckerman, Kieron Burke, Klaus-Robert Muller, Nature Communications 8, (2017). [supplementary information]
[bibtex] [pdf] |

[165] | Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives John C. Snyder, Matthias Rupp, Klaus-Robert Müller, Kieron Burke, International Journal of Quantum Chemistry 115, 1102--1114 (2015).
[bibtex] [pdf] |

[161] | Understanding kernel ridge regression: Common behaviors from simple functions to density functionals Kevin Vu, John C. Snyder, Li Li, Matthias Rupp, Brandon F. Chen, Tarek Khelif, Klaus-Robert Müller, Kieron Burke, International Journal of Quantum Chemistry 115, 1115--1128 (2015).
[bibtex] [pdf] |

[153] | Understanding machine-learned density functionals Li Li, John C. Snyder, Isabelle M. Pelaschier, Jessica Huang, Uma-Naresh Niranjan, Paul Duncan, Matthias Rupp, Klaus-Robert M\FCller, Kieron Burke, International Journal of Quantum Chemistry 116, 819--833 (2016).
[bibtex] [pdf] |

[144] | Orbital-free Bond Breaking via Machine Learning John C. Snyder, Matthias Rupp, Katja Hansen, Leo Blooston, Klaus-Robert Müller, Kieron Burke, J. Chem. Phys. 139, 224104 (2013).
[bibtex] [pdf] |

[142] | Kernels, Pre-Images and Optimization John C. Snyder, Sebastian Mika, Kieron Burke, Klaus-Robert Müller, Chapter in Empirical Inference - Festschrift in Honor of Vladimir N. Vapnik (2013).
[bibtex] [pdf] |

[137] | Finding Density Functionals with Machine Learning John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert Müller, Kieron Burke, Phys. Rev. Lett. 108, 253002 (2012). [supplementary information]
[bibtex] [pdf] |

###### Funding

We graciously acknowledge support from the NSF Grant No. CHE-1240252.