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 highdimensional spaces via induction.
Most DFT research solving the kinetic energy from KohnSham 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 selfconsistent 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 proofofprinciple [Phys. Rev. Lett. 108, 253002 (2012)], we used ML to approximate the kinetic energy functional of particles confined to a onedimensional 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 orbitalfree density functional calculations and abinitio molecular dynamics simulations.
Publications
[176]  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] [doi] 
[175]  Bypassing the KohnSham equations with machine learning Felix Brockherde, Leslie Vogt, Li Li, Mark E Tuckerman, Kieron Burke, KlausRobert Muller, Nature Communications 8, (2016). [supplementary information]
[bibtex] [pdf] 
[165]  Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives John C. Snyder, Matthias Rupp, KlausRobert MÃ¼ller, Kieron Burke, International Journal of Quantum Chemistry 115, 11021114 (2015).
[bibtex] [pdf] [doi] 
[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, KlausRobert MÃ¼ller, Kieron Burke, International Journal of Quantum Chemistry 115, 11151128 (2015).
[bibtex] [pdf] [doi] 
[153]  Understanding machinelearned density functionals Li Li, John C. Snyder, Isabelle M. Pelaschier, Jessica Huang, UmaNaresh Niranjan, Paul Duncan, Matthias Rupp, KlausRobert Müller, Kieron Burke, International Journal of Quantum Chemistry 116, 819833 (2016).
[bibtex] [pdf] [doi] 
[144]  Orbitalfree Bond Breaking via Machine Learning John C. Snyder, Matthias Rupp, Katja Hansen, Leo Blooston, KlausRobert Müller, Kieron Burke, J. Chem. Phys. 139, 224104 (2013).
[bibtex] [pdf] [doi] 
[142]  Kernels, PreImages and Optimization John C. Snyder, Sebastian Mika, Kieron Burke, KlausRobert 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, KlausRobert Müller, Kieron Burke, Phys. Rev. Lett. 108, 253002 (2012). [supplementary information]
[bibtex] [pdf] [doi] 
Funding
We graciously acknowledge support from the NSF Grant No. CHE1240252.
Current Student
Li Li

Kevin Vu

Alumni
John Snyder

Senior Collaborator
KlausRobert MÃ¼ller
