Orbital-free density functional theory calculation applying semi-local machine-learned kinetic energy density functional and kinetic potential

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

doi:10.1016/j.cplett.2020.137358

Cited by 43 publications

(28 citation statements)

References 40 publications

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“…( 8) between KEFDs because we observe that the functional derivative is poorly reproduced when KEDF is trained [40] and this training fails to optimize the electron density in some cases. This problem in the functional derivative leading to the erroneous solution of Euler equation is also reported in the previous efforts to develop KEDF with machine learning [41][42][43][44][45][46][47], where the training set is the KEDF itself. As the training and test sets in the deep learning, we adopt the kinetic energy functional derivative (KEFD) at each real-space grid point.…”

Section: Training Of Neural Network Toward Kinetic Energy Functional ...mentioning

confidence: 63%

Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

Imoto,

Imada,

Oshiyama

2021

Preprint

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Section: Training Of Neural Network Toward Kinetic Energy Functional ...mentioning

confidence: 63%

Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

Imoto,

Imada,

Oshiyama

2021

Preprint

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“…As an example, we show in Figure 7 how the kinetic energy density τ(x) looks like for aluminum, magnesium, and silicon crystals: It is very difficult or impossible to derive analytically an expression for the KEF accurate enough for use in applied simulations of most materials [77]. There is now much progress in machine learning this dependence, in particular, with neural networks but also with other methods, including GPR and some of the methods mentioned earlier [41,[78][79][80][81][82]. This problem is a very stringent test for machine learning methods because the accuracy required here is very high, on the order of a thousandth of a per cent unless there is significant error cancellation.…”

Section: When Are Deep Nns Useful?mentioning

confidence: 98%

“…Approximate formulas for such an expression (𝑇𝑇[𝑓𝑓(𝒙𝒙)]) exist but they are not accurate enough for use in most applications where ab initio modeling is needed, including (organic and inorganic) semiconductors and transition metal containing functional materials of novel energy technologies. In the last several years, substantial progress is being made on this problem with the help of machine learning using, in particular, techniques like neural networks and kernel methods [41,[78][79][80][81][82]. We will return to this example later in the context of deep learning.…”

Section: New Technologies and Challengies Require New Simulation Meth...mentioning

confidence: 99%

Advanced Machine Learning Methods for Learning from Sparse Data in High-Dimensional Spaces: A Perspective on Uses in The Upstream of Development of Novel Energy Technologies

Ihara¹,

Manzhos²

2022

Preprint

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Machine learning (ML) has found increasing use in research on energy conversion and storage technologies, in particular, so-called sustainable technologies. While often ML is used to directly optimize the parameters or phenomena of interest in the space of features, in this perspective, we focus on using ML to construct objects and methods that help in or enable the modeling of the underlying phenomena. We highlight the need for machine learning from very sparse and unevenly distributed numeric data in multidimensional spaces in these applications. After a brief introduction of some common regression-type machine learning techniques, we will focus on more advanced ML techniques which use these known methods as building blocks of more complex schemes and thereby allow working with extremely sparse data and also allow generating insight. Specifically, we will highlight the utility of using representations with sub-dimensional functions by combining the high-dimensional model representation ansatz with machine learning methods like neural networks or Gaussian process regressions in applications ranging from heterogeneous catalysis to nuclear energy.

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“…Moreover, in recent years, significant advances in KEF development, including advances in semi-local (i.e. linear-scaling) KEFs [182,183] as well as machine-learned KEFs [194][195][196][197][198][199][200], are being made. The newest functionals appearing in recent years can treat systems with more non-uniform densities and give hope that in relatively near future many materials used in plasmonics (metals as well as non-metals) can be modeled with OFDFT with at least semi-quantitative accuracy.…”

Section: Real-time Td-ofdftmentioning

confidence: 99%

Modeling of plasmonic properties of nanostructures for next generation solar cells and beyond

Manzhos

Giorgi

Lüder

et al. 2021

Advances in Physics: X

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Plasmonic particles and nanostructures are widely used in photovoltaic and photonics. Surface plasmons were found to enhance different types of solar cells including plasmonic DSSCs, plasmonic solid semiconductor solar cells, plasmonic organic solar cells, and plasmonic perovskite solar cell. Size, composition, and shape of plasmonic nanoparticles as well as nanometer-distance control between particles are key design factors of plasmonic nanostructures. Modeling is rapidly gaining in importance for mechanistic understanding and rational design of plasmonic nanostructures. We review the modeling approaches used to model plasmon resonance features of nanostructures, from classical approaches that can routinely handle most particle sizes used in solar cells to approaches beyond classical electrodynamics such as ab initio approaches based on time-dependent density functional theory (TD-DFT). We highlight recently emerging approaches which have the potential to significantly enhance modeling capabilities in the coming years, in particular, by allowing atomistic (ab initio) modeling at realistic length scales, i.e. of particle sizes beyond 10 nm which are of most interest to plasmonic solar cells but remain problematic with traditional DFT-based techniques, such as density functional tight binding (DFTB) based approaches, time-dependent orbital-free DFT, and machine learning-based approaches, as well as many-body perturbation theory which is expected to gain usage with advances in computing power.

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Orbital-free density functional theory calculation applying semi-local machine-learned kinetic energy density functional and kinetic potential

Cited by 43 publications

References 40 publications

Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

Advanced Machine Learning Methods for Learning from Sparse Data in High-Dimensional Spaces: A Perspective on Uses in The Upstream of Development of Novel Energy Technologies

Modeling of plasmonic properties of nanostructures for next generation solar cells and beyond

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