Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks.

@article{Yao2016KineticEO,
  title={Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks.},
  author={Kun Yao and John A Parkhill},
  journal={Journal of chemical theory and computation},
  year={2016},
  volume={12 3},
  pages={
          1139-47
        }
}
We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from an input electron density. The output of the network is used as a nonlocal correction to conventional local and semilocal kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. The density which minimizes the total energy given by the functional is examined in… 

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References

SHOWING 1-10 OF 103 REFERENCES
Generalized neural-network representation of high-dimensional potential-energy surfaces.
TLDR
A new kind of neural-network representation of DFT potential-energy surfaces is introduced, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT.
Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations.
  • J. Behler
  • Physics
    Physical chemistry chemical physics : PCCP
  • 2011
TLDR
In this Perspective, the current status of NN potentials is reviewed, and their advantages and limitations are discussed.
Understanding Machine-learned Density Functionals
TLDR
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density, and accurate energies are found via a modified Euler-Lagrange constrained minimization of the total energy.
Condition on the Kohn-Sham kinetic energy and modern parametrization of the Thomas-Fermi density.
TLDR
The asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity is studied, presenting a new method to extract the coefficients from oscillating numerical data, and a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms is given.
Orbital-free kinetic-energy density functionals with a density-dependent kernel
We report linear-response kinetic-energy density functionals, which show significant improvement over the Wang-Teter, Perrot, Smargiassi-Madden, Wang-Govind-Carter functionals, yet still maintain
Nonlocal kinetic-energy-density functionals.
TLDR
Nonlocal kinetic-energy functionals within the average density approximation (ADA) framework are presented, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system.
Orbital-free bond breaking via machine learning.
TLDR
Using a one-dimensional model, this nonlinear interpolation between Kohn-Sham reference calculations can accurately dissociate a diatomic, be systematically improved with increased reference data and generate accurate self-consistent densities via a projection method that avoids directions with no data.
Kinetic-energy functional of the electron density.
  • Wang, Teter
  • Physics
    Physical review. B, Condensed matter
  • 1992
TLDR
This quantum oscillation in the electron density is lacking in the densities of previous kinetic-energy functionals and is regarded as the major achievement of the current approach.
Finding Density Functionals with Machine Learning
TLDR
For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities.
Generalized nonlocal kinetic energy density functionals based on the von Weizsäcker functional.
TLDR
The generalized nonlocal von Weizsäcker functionals give very good results for the total kinetic energies and improving the local behavior of the kinetic energy density, resulting in a quasilinear scaling for the computational cost.
...
1
2
3
4
5
...