Highly accurate machine learning model for kinetic energy density functional

Alghadeer, Mohammed; Al-Aswad, Abdulaziz; Alharbi, Fahhad H.

doi:10.1016/j.physleta.2021.127621

Cited by 11 publications

(7 citation statements)

References 39 publications

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“…Because their explicit form typically is not known, they do not fit easily into the one-point, two-point categorization, though some are built specifically to have a certain maximum order of density gradients. Just as machine learning itself is relatively recent, so also the literature of ML KEDFs is comparatively recent and small. ,,− …”

Section: Introductionmentioning

confidence: 99%

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

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Kohn−Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of firstprinciples molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn−Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, twopoint, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

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Section: Introductionmentioning

confidence: 99%

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

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“…A radically different use of ML consists of improving the theory at its core instead of targeting the DFT outputs. For instance, ML can be used to numerically design new energy density functionals, effectively producing fully exchange and correlation energies [46][47][48][49][50][51], and kinetic energy densities [52][53][54][55]. These strategies, in general, seek to find more accurate approximations to the DFT energy, going beyond the current approximations [56], or to eliminate the need of introducing the KS construct by replacing the self-consistent KS equations with a direct minimization of the functional [6].…”

Section: Introductionmentioning

confidence: 99%

Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations

Focassio

Domina

Patil

et al. 2023

Preprint

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As the go-to method to solve the electronic structure problem, Kohn-Sham density functional theory (KS-DFT) can be used to obtain the ground-state charge density, total energy, and several other key materials' properties. Unfortunately, the solution of the Kohn-Sham equations is found iteratively. This is a numerically intensive task, limiting the possible size and complexity of the systems to be treated. Machine-learning (ML) models for the charge density can then be used as surrogates to generate the converged charge density and reduce the computational cost of solving the electronic structure problem. We derive a powerful grid-centred structural representation based on the Jacobi and Legendre polynomials that, combined with a linear regression built on a dataefficient workflow, can accurately learn the charge density. Then, we design a machine-learning pipeline that can return energy and forces at the quality of a converged DFT calculation but at a fraction of the computational cost. This can be used as a tool for the fast scanning of the energy landscape and as a starting point to the DFT self-consistent cycle, in both cases maintaining a low computational cost.

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“…In physics-guided machine learning implementations, it is essential to set-in advance-a vector space (in term of features) to which the targeted quantities should be projected [24]. The commonly used spaces are based on GGA and meta-GGA [25,26], kernels [27][28][29][30], and special expansions [31]. It is also important to mention that there are other implementations, which are not principally physics-guided and are mostly based on neural networks (NN) [32,33].…”

Section: Introductionmentioning

confidence: 99%

Constraint‐based analysis of a physics‐guided kinetic energy density expansion

Aldossari

Alenaizan

Al-Aswad

et al. 2022

Int J of Quantum Chemistry

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An approach guided by physical consistency in determining the general forms of D‐dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one‐point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as r→∞. This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.

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Highly accurate machine learning model for kinetic energy density functional

Cited by 11 publications

References 39 publications

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations

Constraint‐based analysis of a physics‐guided kinetic energy density expansion

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