Saturday, March 31, 2012

Finding Density Functionals with Machine Learning

John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert Müller, and Kieron Burke arXiv:1112.5441v1 2012 (Open Access)

The study uses standard machine learning (ML) techniques to construct a density-based (i.e. orbital-free) expression for the electronic kinetic energy $(T^{ML})$ for a model 1-dimensional system of up to four non-interacting electrons subject to a smooth potential.  Sub-kcal/mol accuracy can be achieved with fewer than 100 Gaussian training densities.

Numerical noise in the functional derivative of $T^{ML}$ is removed by a principal component analysis and while variational minimization of the energy fails to find a unique density "the search does not produce a unique minimum, it produces a range of similar but valid approximate densities, each with a small error."

While the application of the method does not require any physical intuition about the form of the functional, physically motivated potentials can be included in the method to improve results.  It will be very interesting indeed to see this and similar approaches being trained against highly accurate electronic structure data computed for for atoms and molecules, not just for the kinetic energy but for the exchange-correlation functional itself.

Acknowledgement: I thank Matteo Cavalleri for bringing this paper to my attention via twitter.

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