Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization

Yu, Maituo; Yang, Shuyang; Wu, Chunzhi; Marom, Noa

doi:10.1038/s41524-020-00446-9

Cited by 128 publications

(132 citation statements)

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“…It was later discovered that the Hubbard U parameter corrects for SIE, which is present in not only d and f , but also s and p states [91,92]. While light elements (e.g., O, N, S) contain only s and p states and thus do not have as large SIE as TM, the U correction has been increasingly applied to light elements in recent years to improve the computational prediction of properties, such as the band gap [78,93,94]. Additionally, in the literature, U has been applied to d 10 elements from the p-block (specifically group III-IV) of the periodic table, such as Ga 2+ [35].…”

Section: Introductionmentioning

confidence: 99%

“…While elements, like Ga 2+ , are not TM, they have electronic configurations that match that of a d 10 TM under certain ionizations. Applying U to light elements and/or d 10 group III-IV elements (e.g., Ge, In, Sn, Pb) is still in debate in the literature [35,78,93,94]. This question will be addressed in this work using DFPT [79], and in particular we will explore the sensitivity of band gaps to the application of the Hubbard U correction to p states of light elements.…”

Section: Introductionmentioning

confidence: 99%

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Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

et al. 2021

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Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initioU parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

et al. 2021

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“…This severely limits the utility of conventional DFT for entire classes of quantum materials. A very promising emerging research area addresses this challenge by using ML methods to systematically improve the approximations made in DFT calculations [42][43][44][45] . AI methods are also being used to accelerate high-level methods such as Quantum Monte Carlo (QMC) 46,47 and Dynamical Mean Field Theory (DMFT) 48 , which are more accurate than DFT but can be orders-of-magnitude slower and higher in computational cost.…”

Section: Ai For Computational Quantum Materialsmentioning

confidence: 99%

Artificial intelligence for search and discovery of quantum materials

et al. 2021

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Artificial intelligence and machine learning are becoming indispensable tools in many areas of physics, including astrophysics, particle physics, and climate science. In the arena of quantum materials, the rise of new experimental and computational techniques has increased the volume and the speed with which data are collected, and artificial intelligence is poised to impact the exploration of new materials such as superconductors, spin liquids, and topological insulators. This review outlines how the use of data-driven approaches is changing the landscape of quantum materials research. From rapid construction and analysis of computational and experimental databases to implementing physical models as pathfinding guidelines for autonomous experiments, we show that artificial intelligence is already well on its way to becoming the lynchpin in the search and discovery of quantum materials.

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“…Active learning refers to the idea of a machine learning algorithm "learning" from data, proposing next experiments or calculations, and improving prediction accuracy with fewer training data or lower cost. 2 Bayesian Optimization (BO), an active learning framework, often used to tune hyperparameters in machine learning models, has seen a rise in its applications to various chemical science fields, including parameter tuning for density functional theory (DFT) calculations, 3 catalyst synthesis, 4,5 high throughput reactions, 6 and computational material discovery. [7][8][9] Its close variant, kriging, 10 originating in geostatistics, has also been widely applied in process engineering.…”

Section: Introductionmentioning

confidence: 99%

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Wang

Chen²,

Vlachos³

2021

Preprint

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<div> <div> <div> <p>Automation and optimization of chemical systems require well-inform decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. We introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian Optimization algorithms and supports both automated and human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub. </p> </div> </div> </div>

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Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization

Cited by 128 publications

References 57 publications

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Artificial intelligence for search and discovery of quantum materials

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

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