Pure density functional for strong correlation and the thermodynamic limit from machine learning

Li, Li; Baker, Thomas E.; White, Steven R.; Burke, Kieron

doi:10.1103/physrevb.94.245129

Cited by 108 publications

(85 citation statements)

References 42 publications

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“…For decades, one of the main bottlenecks of molecular simulations has been the calculation of the density functionals. As in numerous fields, machine learning constitutes a promising avenue for the fast and efficient evaluation of these functionals without recourse to explicit calculations Advances in Chemistry 13 [17,24,25,60]. Here, the density functional is simply learned from existing examples with machine learning techniques.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, it has been proposed to evaluate the functional density with machine learning techniques. The functional density is learned by examples instead of directly solving the Kohn-Sham equations [17,24,25]. As a result, substantially less time is required to complete the calculations allowing for larger system to be simulated and longer time-scales to be explored.…”

Section: Exchange-correlation Energymentioning

confidence: 99%

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Computational Methods for Ab Initio Molecular Dynamics

Paquet

Viktor

2018

Advances in Chemistry

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Ab initio molecular dynamics is an irreplaceable technique for the realistic simulation of complex molecular systems and processes from first principles. This paper proposes a comprehensive and self-contained review of ab initio molecular dynamics from a computational perspective and from first principles. Quantum mechanics is presented from a molecular dynamics perspective. Various approximations and formulations are proposed, including the Ehrenfest, Born-Oppenheimer, and Hartree-Fock molecular dynamics. Subsequently, the Kohn-Sham formulation of molecular dynamics is introduced as well as the afferent concept of density functional. As a result, Car-Parrinello molecular dynamics is discussed, together with its extension to isothermal and isobaric processes. Car-Parrinello molecular dynamics is then reformulated in terms of path integrals. Finally, some implementation issues are analysed, namely, the pseudopotential, the orbital functional basis, and hybrid molecular dynamics.

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Section: Discussionmentioning

confidence: 99%

Section: Exchange-correlation Energymentioning

confidence: 99%

Computational Methods for Ab Initio Molecular Dynamics

Paquet

Viktor

2018

Advances in Chemistry

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“…We now present a relatively chronological list used in recent materials research, which is considerable but not exhaustive. These include: bondorientational order parameters (BOP) [243]; Behler-Parrinello atom-centered symmetry functions (ACSF) [233,244], and its modified [245] and weighted (wACSF) [246] versions; Gaussian Approximation Potentials (GAP) [212,232] using smooth overlap of atomic positions (SOAP) [213] also extended for tensorial properties [247]; Coulomb matrix [248] and Bag of Bonds (BOB) [249], and the subsequent interatomic many body expansions (MBE) [250,251] like the so-called BAML (bonds, angles machine learning) [252] and fixed-size inverse distances [253]; metric fingerprints [238]; bispectrum [213]; atomic local frame (ALF) [254]; partial radial and angular distribution functions (PRDF, ADF) [255] and generalized radial distribution functions (GRDF) [224]; Fourier series of radial distribution functions [256]; force vectors representations [257]; spectral neighbor analysis potential (SNAP) [258]; permutation invariant polynomials [245]; particle densities [259]; angular Fourier series (AFS) [213]; topological polyhedra [260], Voronoi [261] and Voronoi-Dirichlet [262] tessellations; spherical harmonics [263]; histogram of distances, angles, or dihedral angles [264]; classical forcefield-inspired descriptors (CFID) [209]; graph-based such as Graph Approximated Energy (GRAPE) [265]; constant complexity descriptors based on Chebyshev polynomials [266]; symmetrized gradient-domain machine learning ...…”

Section: Representations and Descriptorsmentioning

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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“…In physics, the application of neural networks, and machine learning in general, to many-body quantum mechanics is a novel and burgeoning field of research [1]. Currently, there are three main lines of pursuit: the application of machine learning to the problem of classifying various phases of matter [2][3][4][5][6][7][8][9], accelerating material searches and design [10][11][12][13], and the quest to encode quantum mechanical states in structures mimicking the setup of a neural network [14][15][16]. This work is concerned with the first kind of approach.…”

Section: Introductionmentioning

confidence: 99%

Probing many-body localization with neural networks

2017

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We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.

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Pure density functional for strong correlation and the thermodynamic limit from machine learning

Cited by 108 publications

References 42 publications

Computational Methods for Ab Initio Molecular Dynamics

Computational Methods for Ab Initio Molecular Dynamics

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

Probing many-body localization with neural networks

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