A deep learning method for computing eigenvalues of the fractional Schrödinger operator (Q6130977)

scientific article; zbMATH DE number 7827309

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English	A deep learning method for computing eigenvalues of the fractional Schrödinger operator	scientific article; zbMATH DE number 7827309

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instance of

scholarly article

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title

A deep learning method for computing eigenvalues of the fractional Schrödinger operator (English)

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Journal of Systems Science and Complexity

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publication date

3 April 2024

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full work available at URL

https://arxiv.org/abs/2308.13986

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zbMATH Keywords

eigenvalue problem

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deep learning

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fractional Schrödinger operator

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isospectral problem

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MaRDI profile type

MaRDI publication profile

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cites work

The random walk's guide to anomalous diffusion: A fractional dynamics approach

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A fractional porous medium equation

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Fractional quantum mechanics and Lévy path integrals

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Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver

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Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

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Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments

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Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations

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Unbiased ‘walk-on-spheres’ Monte Carlo methods for the fractional Laplacian

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A Walk Outside Spheres for the fractional Laplacian: Fields and first eigenvalue

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Numerical methods for nonlocal and fractional models

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What is the fractional Laplacian? A comparative review with new results

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Numerical methods for fractional diffusion

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Eigenvalues of the fractional Laplace operator in the unit ball

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Fractional calculus for power functions and eigenvalues of the fractional Laplacian

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A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrödinger operator

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Finite element approximation for the fractional eigenvalue problem

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A neural network for computing eigenvectors and eigenvalues

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Neural networks for computing eigenvalues and eigenvectors

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Solving the quantum many-body problem with artificial neural networks

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Solving many-electron Schrödinger equation using deep neural networks

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Solving high-dimensional eigenvalue problems using deep neural networks: a diffusion Monte Carlo like approach

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A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks

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Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

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A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems

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Ten equivalent definitions of the fractional Laplace operator

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From the long jump random walk to the fractional Laplacian

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Eigenvalue Bounds for the Fractional Laplacian: A Review

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Two-sided eigenvalue estimates for subordinate processes in domains

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Fundamental gaps of the fractional Schrödinger operator

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Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators

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Solving for high-dimensional committor functions using artificial neural networks

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Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape

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Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods

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Can One Hear the Shape of a Drum?

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One cannot hear the shape of a drum

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Isospectral plane domains and surfaces via Riemannian orbifolds

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Eigenmodes of Isospectral Drums

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Algebraic multigrid methods for solving generalized eigenvalue problems

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Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential

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Identifiers

arXiv ID

2308.13986

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DOI

10.1007/s11424-024-3250-9

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6130977