Orbital-free bond breaking via machine learning

Snyder, John C.; Rupp, Matthias; Hansen, Katja; Blooston, Leo; Müller, Klaus Robert; Burke, Kieron

doi:10.1063/1.4834075

Cited by 117 publications

(131 citation statements)

References 47 publications

Supporting

Mentioning

120

Contrasting

Order By: Relevance

“…But its functional derivatives are so poor that they are totally unusable for finding a self-consistent solution. Several techniques have been developed which constrain a minimization to stay on the manifold of densities on which the machine-learned functional is accurate [SRHB13;SMBM13]. These lead to algorithms that produce accurate densities, although the density-driven error is up to 10 times greater than the functional error, and the solutions also are slightly dependent on the starting point.…”

Section: Pure Dftmentioning

confidence: 99%

The Importance of Being Inconsistent

Wasserman

Nafziger

Jiang

et al. 2017

Annu. Rev. Phys. Chem.

Self Cite

114

156

View full text Add to dashboard Cite

We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using 'better' densities. We review the history of these approaches, many of their applications, and give simple pedagogical examples.

show abstract

Section: Pure Dftmentioning

confidence: 99%

The Importance of Being Inconsistent

Wasserman

Nafziger

Jiang

et al. 2017

Annu. Rev. Phys. Chem.

Self Cite

114

156

View full text Add to dashboard Cite

show abstract

“…Semi-empirical optimization lends itself well as a method for finding reasonably accurate compromises, but will never completely eliminate DFT errors. Even so, recent developments 23,24 clearly indicate that advanced machine learning methods have great potential for generating accurate density functionals. The BEEF class of functionals combines machine learning with a Bayesian point of view to generalize the fitting procedure for XC functionals, thereby allowing for estimation of the errors on calculated quantities.…”

Section: Introductionmentioning

confidence: 99%

mBEEF: An accurate semi-local Bayesian error estimation density functional

Wellendorff

Lundgaard

Jacobsen

et al. 2014

The Journal of Chemical Physics

148

173

View full text Add to dashboard Cite

Adsorption of transition-metal atoms on boron nitride nanotube: A density-functional study J. Chem. Phys. 125, 044711 (2006) (2012)]. The functional is designed to give reasonably accurate density functional theory (DFT) predictions of a broad range of properties in materials physics and chemistry, while exhibiting a high degree of transferability. Particularly, it improves upon solid cohesive energies and lattice constants over the BEEF-vdW functional without compromising high performance on adsorption and reaction energies. We thus expect it to be particularly well-suited for studies in surface science and catalysis. An ensemble of functionals for error estimation in DFT is an intrinsic feature of exchange-correlation models designed this way, and we show how the Bayesian ensemble may provide a systematic analysis of the reliability of DFT based simulations.

show abstract

“…It would be very interesting to combine our procedure with concepts from recent works on machine learning of density functionals [31][32][33][34][35][36]. On the one hand, these works typically required less training densities than our approach.…”

Section: Discussionmentioning

confidence: 99%

Systematic construction of density functionals based on matrix product state computations

et al. 2016

View full text Add to dashboard Cite

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz whose non-locality can be increased systematically. Second, we present a fitting strategy that is based on systematically increasing a reasonably chosen set of training densities. We investigate our procedure in the context of strongly correlated fermions on a onedimensional lattice in which we compute accurate training densities with the help of matrix product states. Focusing on the exchange-correlation energy, we demonstrate how an efficient approximation can be found that includes and systematically improves beyond the local density approximation. Importantly, this systematic improvement is shown for target densities that are quite different from the training densities.

show abstract

Orbital-free bond breaking via machine learning

Cited by 117 publications

References 47 publications

The Importance of Being Inconsistent

The Importance of Being Inconsistent

mBEEF: An accurate semi-local Bayesian error estimation density functional

Systematic construction of density functionals based on matrix product state computations

Contact Info

Product

Resources

About