Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density

Seino, Junji; Kageyama, Ryo; Fujinami, Mikito; Ikabata, Yasuhiro; Nakai, Hiromi

doi:10.1063/1.5007230

Cited by 87 publications

(64 citation statements)

References 61 publications

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“…The general idea is presented in figure 16(left). A prominent example and intuitive approach is using ML to predict novel density functionals to be used within DFT, which can be readily used with current implementations [259,[274][275][276][277]. The functionals to be predicted can be the exchange-correlation as used in the traditional DFT KS mapping, or of the orbital-free type.…”

Section: Novel ML Methods In Physics and Materialsmentioning

confidence: 99%

From DFT to machine learning: recent approaches to materials science–a review

et al. 2019

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Recent advances in experimental and computational methods are increasing the quantity and complexity of generated data. This massive amount of raw data needs to be stored and interpreted in order to advance the materials science field. Identifying correlations and patterns from large amounts of complex data is being performed by machine learning algorithms for decades. Recently, the materials science community started to invest in these methodologies to extract knowledge and insights from the accumulated data. This review follows a logical sequence starting from density functional theory as the representative instance of electronic structure methods, to the subsequent high-throughput approach, used to generate large amounts of data. Ultimately, data-driven strategies which include data mining, screening, and machine learning techniques, employ the data generated. We show how these approaches to modern computational materials science are being used to uncover complexities and design novel materials with enhanced properties. Finally, we point to the present research problems, challenges, and potential future perspectives of this new exciting field. characterized by its diverse and huge volume, usually ranging from terabytes to petabytes of data, being created in or near real-time. Such data is found either structured and unstructured in nature, and is exhaustive, usually aiming to capture entire populations in a scalable manner [7]. Simple tasks represent challenges in this scale: capture, curation, storage, search, sharing, analysis, and visualization of the data cannot be accomplished without the proper tools. Thus, it can be effectively summarized by the popular 'five V's': volume, velocity, variety, veracity, and value, shown in figure 3(right). A related sixth V is visualization, although not exclusive to Big Data, which requires different techniques to handle data with various characteristics.Striving to tackle the challenges imposed by Big Data, the field of Data Science has arisen. It is largely interdisciplinary being a combination of mathematics and statistics, computer science and programming, and domain knowledge for problem definition and solving, as shown in figure 3(left). Its objective is, roughly speaking, to deal with the whole process of data production, cleaning, preparation, and finally, analysis. Data science encompasses areas such as Big Data, which deals with large volumes of data, and data mining, which relates to analysis processes to discover patterns and extract knowledge from data, part of the so-called Knowledge Discovery in Databases (KDD).The analysis process within Data Science is challenging, as the techniques are very different from traditional static and rigid datasets, generated and analyzed under a predetermined hypothesis. The distinction from traditional data is based on the larger abundance, exhaustivity, and variety of Big Data. It is also much more dynamic, messy and uncertain, being highly relational [7]. Recently, the possibility of overcoming such a challenge slowly sta...

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Section: Novel ML Methods In Physics and Materialsmentioning

confidence: 99%

From DFT to machine learning: recent approaches to materials science–a review

et al. 2019

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“…where C TF = (3/10) 3π 2 2/3 . With respect to the exact values (T KS s ), the TF functional leads to underestimations for atoms 42 and molecules [43][44][45][46] of about 10%. Since the kinetic energy is a major component of the total energy E tot (from the virial theorem T s ≈ −E tot ) such errors are extremely large.…”

Section: A Orbital-free Kinetic Energy Densitiesmentioning

confidence: 99%

Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids

Tran

Kovács

Kalantari

et al. 2018

The Journal of Chemical Physics

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A recent study of Mejia-Rodriguez and Trickey [Phys. Rev. A 96, 052512 (2017)] showed that the deorbitalization procedure (replacing the exact Kohn-Sham kinetic-energy density by an approximate orbital-free expression) applied to exchange-correlation functionals of the meta-generalized gradient approximation (MGGA) can lead to important changes in the results for molecular properties. For the present work, the deorbitalization of MGGA functionals is further investigated by considering various properties of solids. It is shown that depending on the MGGA, common orbitalfree approximations to the kinetic-energy density can be sufficiently accurate for the lattice constant, bulk modulus, and cohesive energy. For the band gap, calculated with the modified Becke-Johnson MGGA potential, the deorbitalization has a larger impact on the results.

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“…Nakai group also produced accurate NN fits to KS KEDs [118]. They used electron densities and their gradients up to the third order as descriptors and fitted the enhancement factor.…”

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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Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density

Cited by 87 publications

References 61 publications

From DFT to machine learning: recent approaches to materials science–a review

From DFT to machine learning: recent approaches to materials science–a review

Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids

Machine learning for the solution of the Schrödinger equation

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