Machine Learning the Physical Nonlocal Exchange–Correlation Functional of Density-Functional Theory

Schmidt, Jonathan; Benavides-Riveros, Carlos L.; Marques, Miguel A. L.

doi:10.1021/acs.jpclett.9b02422

Cited by 88 publications

(79 citation statements)

References 56 publications

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“…Recently, machine-learning (ML)-based DFAs have been shown to break the constraints of Jacob's ladder, offering highly accurate, pure, and non-local density functionals for different one-dimensional model systems [10][11][12][13] . Although these approaches show that it is possible to learn the highly non-linear mapping from the electron density to the energy from data, they cannot be directly transferred to real systems.…”

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confidence: 99%

Pure non-local machine-learned density functional theory for electron correlation

Margraf

2021

Nat Commun

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Density-functional theory (DFT) is a rigorous and (in principle) exact framework for the description of the ground state properties of atoms, molecules and solids based on their electron density. While computationally efficient density-functional approximations (DFAs) have become essential tools in computational chemistry, their (semi-)local treatment of electron correlation has a number of well-known pathologies, e.g. related to electron self-interaction. Here, we present a type of machine-learning (ML) based DFA (termed Kernel Density Functional Approximation, KDFA) that is pure, non-local and transferable, and can be efficiently trained with fully quantitative reference methods. The functionals retain the mean-field computational cost of common DFAs and are shown to be applicable to non-covalent, ionic and covalent interactions, as well as across different system sizes. We demonstrate their remarkable possibilities by computing the free energy surface for the protonated water dimer at hitherto unfeasible gold-standard coupled cluster quality on a single commodity workstation.

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confidence: 99%

Pure non-local machine-learned density functional theory for electron correlation

Margraf

2021

Nat Commun

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“…The first relies on the pragmatic application of system-dependent machine learning corrections to the interaction energy of approximate functionals with, for instance, ∆-ML. The second approach, which has been successfully applied to two-electrons, one-dimensional systems, 116…”

Section: Resultsmentioning

confidence: 99%

Balancing DFT Interaction Energies in Charged Dimers Precursors to Organic Semiconductors

Fabrizio¹,

Petraglia²,

Corminbœuf³

2019

Preprint

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Accurately describing intermolecular interactions within the framework of Kohn-Sham density functional theory (KS-DFT) has resulted in numerous benchmark databases over the past two decades. By far, the largest efforts have been spent on closed-shell, neutral dimers for which today, the interaction energies and geometries can be accurately reproduced by various combinations of dispersion-corrected density functional approximations (DFAs). In sharp contrast, charged, open-shell dimers remain a challenge as illustrated by the analysis of the OREL26rad benchmark set consisting of pi-dimer radical cations. Aside from the methodological aspect, achieving a proper description of radical cationic complexes is appealing due to their role as models for charge carriers in organic semiconductors. In the interest of providing an assessment of more realistic dimer systems, we construct a dataset of large radical cationic dimers (CryOrel) and jointly train the 19 parameters of a dispersion corrected, range-separated hybrid density functional (wB97X-dDsC), with the objective of providing the maximum balance between the treatment of long-range London dispersion and reduction of the delocalization error. These conditions are essential to obtain accurate energy profiles and binding energies of charged, open-shell dimers. Comparisons with the performance of the parent wB97X functional series and state-of-the-art wavefunction based methods are provided. <br>

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“…The ML methods considered above are ignorant of symmetry. This can be addressed by explicit or implicit symmetrization [46,98,136,157]. ML typically requires relatively costly optimization of parameters (NN) or hyper-parameters (GPR, KRR) or extensive evolutionary searches (GA-inspired schemes).…”

Section: Discussionmentioning

confidence: 99%

“…Custodio et al [97] used single-and two-hidden layer NN to learn an LSDA type functional for a one-dimensional Hubbard model. Schmidt et al [98] used a neural network to learn the universal exchange-correlation functional that simultaneously reproduces both the exact exchange-correlation energy and the potential, for a one-dimensional system with two strongly correlated electrons, in a non-singular potential. A multi-layer NN was used with exponential linear neurons (rather than common sigmoidal neurons), and symmetry was inbuilt into it by fixing of first layer weights.…”

Section: Exchange-correlation 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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Machine Learning the Physical Nonlocal Exchange–Correlation Functional of Density-Functional Theory

Cited by 88 publications

References 56 publications

Pure non-local machine-learned density functional theory for electron correlation

Pure non-local machine-learned density functional theory for electron correlation

Balancing DFT Interaction Energies in Charged Dimers Precursors to Organic Semiconductors

Machine learning for the solution of the Schrödinger equation

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