Can exact conditions improve machine-learned density functionals?

Hollingsworth, Jacob; Baker, Thomas E.; Burke, Kieron

doi:10.1063/1.5025668

Cited by 55 publications

(55 citation statements)

References 37 publications

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“…The original ML model for the KEDF has been shown to successfully describe bond breaking 26 and was extended to include basis set independence 27 as well as scale-invariance conditions. 28 The same ML model has also been employed for direct fits of F [ n ], the universal part of the total energy density functional. 29 A very interesting ML model was investigated by Yao and Parkhill, who used a 1D convolutional neural network to fit the kinetic energy as a function of the density projected onto bond directions.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative

Meyer

Weichselbaum

Hauser

2020

J. Chem. Theory Comput.

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Orbital-free approaches might offer a way to boost the applicability of density functional theory by orders of magnitude in system size. An important ingredient for this endeavor is the kinetic energy density functional. Snyder et al. [ 253002 23004593 Phys. Rev. Lett. 2012 108 ] presented a machine learning approximation for this functional achieving chemical accuracy on a one-dimensional model system. However, a poor performance with respect to the functional derivative, a crucial element in iterative energy minimization procedures, enforced the application of a computationally expensive projection method. In this work we circumvent this issue by including the functional derivative into the training of various machine learning models. Besides kernel ridge regression, the original method of choice, we also test the performance of convolutional neural network techniques borrowed from the field of image recognition.

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Section: Introductionmentioning

confidence: 99%

Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative

Meyer

Weichselbaum

Hauser

2020

J. Chem. Theory Comput.

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“…In this paper, we describe an approach for generating an ML framework that satisfies the criteria outlined above. The ML model employed in this work is kernel ridge regression (KRR), the basic principles of which in the construction of density functionals have been developed over several years [63][64][65][66][67][68][69] . In order to advance our ML framework 53 to the prediction of coupledcluster (CC) energies, as opposed to DFT energies, one need only recognize that the basic ML construction procedure is independent of the source of inputs.…”

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confidence: 99%

Quantum chemical accuracy from density functional approximations via machine learning

et al. 2020

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Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol−1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol−1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT is highlighted by correcting “on the fly” DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

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“…Non-linearity of the NN fit was mild (most of the KED variance could be captured by a linear fit); as a result, the exact conditions were, if one can say so, 'nearly satisfied' . Burke and co-workers showed on one-dimensional synthetic problems that the use of scaled variables may or may not improve machine-learned KEFs [120]; they used the KRR method. It appears that using non-scaled variables is a useful line of exploration which should not be ignored, as exact uniform density scaling does not happen in Nature.…”

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Machine learning for the solution of the Schrödinger equation

Manzhos

2020

Mach. Learn.: Sci. Technol.

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Machine learning (ML) methods have recently been increasingly widely used in quantum chemistry. While ML methods are now accepted as high accuracy approaches to construct interatomic potentials for applications, the use of ML to solve the Schrödinger equation, either vibrational or electronic, while not new, is only now making significant headway towards applications. We survey recent uses of ML techniques to solve the Schrödinger equation, including the vibrational Schrödinger equation, the electronic Schrödinger equation and the related problems of constructing functionals for density functional theory (DFT) as well as potentials which enter semi-empirical approximations to DFT. We highlight similarities and differences and specific difficulties that ML faces in these applications and possibilities for cross-fertilization of ideas.© 2020 The Author(s). Published by IOP Publishing Ltd Mach. Learn.: Sci. Technol. 1 (2020) 013002 S Manzhos approximator properties, with modifications specific to the problem of solving the SE or building functionals, including adapted architectures of ML methods and data selection schemes. It is therefore important to recognize similarities and differences in the requirements that can be addressed via ML among different applications.In this Perspective, we survey recent uses of ML techniques to solve the Schrödinger equation, including the vibrational Schrödinger equation and the electronic problem: the electronic Schrödinger equation and the related problems of constructing exchange-correlation and kinetic energy functionals for Kohn-Sham (KS-) and orbital-free (OF-) density functional theory (DFT) as well as use of ML for semi-empirical approximations used in density functional based approaches such as DFTB (density functional tight binding) and dispersion-corrected DFT (DFT-D). We only consider the use of ML for the solution of the vibrational and electronic SE or the KS equation or the Hohenberg-Kohn (HK) equation and not methods that aim to avoid such solutions (such as those directly mapping the molecular structure to the spectrum or energy or properties without solving for the density or wavefunction [29][30][31][32][33][34][35][36]); we also do not consider uses of ML for other types of quantum mechanical modelling or other types of differential or integral equations [37][38][39][40][41][42].We do not aim to present a comprehensive review but rather a survey allowing similarities and differences of ML uses in all these applications, as well as promising directions for future research, to transpire. This is not a review of ML methods; the key machine learning techniques that found use in quantum chemistry are well reviewed elsewhere [3-5, 43, 44], their description will not be repeated there; the reader is advised to consult the literature for their introduction, such as [45,46] for neural networks, [47,48] for Gaussian process regression (GPR), [49] for kernel ridge regression (KRR; note the similarity in the form of the function representation between GPR and KRR), [50] for...

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Can exact conditions improve machine-learned density functionals?

Cited by 55 publications

References 37 publications

Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative

Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative

Quantum chemical accuracy from density functional approximations via machine learning

Machine learning for the solution of the Schrödinger equation

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