Understanding Machine-learned Density Functionals
By Li Li, John C. Snyder, Isabelle M. Pelaschier, Jessica Huang, Uma-Naresh Niranjan, Paul Duncan, Matthias Rupp , K. Müller, Kieron Burke. 2014
164 citations recorded by the source corpus.
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. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densities} are found via a modified Euler-Lagrange constrained minimization of the total energy. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed.
Subfields: Materials Chemistry, Spectroscopy
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Materials Chemistry
- K. Müller
- Kieron Burke
- Matthias Rupp
- John C. Snyder
- Bryan R. Goldsmith
- Christopher J. Bartel
- Christopher Sutton
- Jin-Xun Liu
In Spectroscopy
- Bryan R. Goldsmith
- J. Esterhuizen
- Christopher Sutton
- Christopher J. Bartel
- Jin-Xun Liu
- K. Müller
- Kieron Burke
- Matthias Rupp
Citations in the corpus
- Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, methodology): “To overcome this limitation, a modified Euler-Lagrange constraint was proposed in [26], which restricted the space of n 0 ( r ) to the density manifold observed in the training set.”
- Machine learning for heterogeneous catalyst design and discovery (2018, background): “74,96 Many thousands of scientific articles published each year use QM methods, so these types of machine learning works are exciting because they promise to allow the construction of fast potentials with QM accuracy to simulate catalyst systems.”
- Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives (2015, methodology): “[8, 9, 17, 18], because they interpolate among very limited data, never produce accurate functional derivatives.”
- Convolutional neural networks for atomistic systems (2017, methodology): “Additional works include using a Coulomb matrix to make predictions of atomization energies [26], and understanding of machine learning density functionals [27].”