Machine learning electron correlation in a disordered medium

Ma, Jianhua; Zhang, Puhan; Tan, Yaohua; Ghosh, Avik W.; Chern, Gia-Wei

doi:10.1103/physrevb.99.085118

Cited by 19 publications

(17 citation statements)

References 66 publications

(89 reference statements)

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“…Nagai et al [95] used a multi-layer NN to map the electron density to the Hartree-exchange-correlation potential for a test system-a one-dimensional two-particle spinless fermion model. A multi-layer NN was also used to learn the electron correlation in the Anderson-Hubbard model by Ma et al [96]. Custodio et al [97] used single-and two-hidden layer NN to learn an LSDA type functional for a one-dimensional Hubbard model.…”

Section: Exchange-correlation 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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Section: Exchange-correlation Functionalsmentioning

confidence: 99%

Machine learning for the solution of the Schrödinger equation

Manzhos

2020

Mach. Learn.: Sci. Technol.

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“…For these an exact solution typically does not exist, except for a few limiting cases, while exact diagonalization is bound by the severe scaling of the Hilbert space with the system size, and hence by the computational costs. For instance, ML has been used to find ground-state properties and observables of fermion-boson coupled Hamiltonians [13], disordered Hubbard-Anderson models [14] and a variety of spin models [15][16][17]. At the same time some progress has been made in classifying quantum states at finite temperature and thus identifying phase transitions [18,19].…”

Section: Introductionmentioning

confidence: 99%

Machine-learning semilocal density functional theory for many-body lattice models at zero and finite temperature

2021

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We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site occupation and the total energy, which is then minimized at the ground-state occupation.In contrast, at finite temperature the same relation is defined between the Helmholtz free energy and the equilibrium site occupation. Most importantly, both functionals are semilocal, so that they are independent from the size of the system under investigation and can be constructed over exact data for small systems. These "exact" functionals are numerically defined by neural networks. We also define additional neural networks for finite-temperature thermodynamical quantities, such as the entropy and heat capacity. These can be either a functional of the ground-state site occupation or of the finite-temperature equilibrium site occupation. In the first case their equilibrium value does not correspond to an extremal point of the functional, while it does in the second case. Our work gives us access to finite-temperature properties of many-body systems in the thermodynamic limit.

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“…For these an exact solution typically does not exist, except for a few limiting cases, while exact diagonalisation is bound by the severe scaling of the Hilbert space with the system size, and hence by the computational costs. For instance, ML has been used to find ground-state properties and observables of fermion-boson coupled Hamiltonians, 13 disordered Hubbard-Anderson models 14 and a variety of spin models. [15][16][17] At the same time some progress has been made in classifying quantum states at finite temperature and thus identifying phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Machine-learning semi-local density functional theory for many-body lattice models at zero and finite temperature

Nelson,

Tiwari,

Sanvito

2021

Preprint

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We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation between the site occupation and the total energy, which is then minimised at the ground-state occupation. In contrast, at finite temperature the same relation is defined between the Helmholtz free energy and the equilibrium site occupation. Most importantly, both functionals are semi-local, so that they are independent from the size of the system under investigation and can be constructed over exact data for small systems. These 'exact' functionals are numerically defined by neural networks. We also define additional neural networks for finitetemperature thermodynamical quantities, such as the entropy and heat capacity. These can be either a functional of the ground-state site occupation or of the finite-temperature equilibrium site occupation. In the first case their equilibrium value does not correspond to an extremal point of the functional, while it does in the second case. Our work gives us access to finite-temperature properties of many-body systems in the thermodynamic limit.

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Machine learning electron correlation in a disordered medium

Cited by 19 publications

References 66 publications

Machine learning for the solution of the Schrödinger equation

Machine learning for the solution of the Schrödinger equation

Machine-learning semilocal density functional theory for many-body lattice models at zero and finite temperature

Machine-learning semi-local density functional theory for many-body lattice models at zero and finite temperature

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