An optimization-based approach to parameter learning for fractional type nonlocal models (Q2147289)

scientific article; zbMATH DE number 7546669

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English	An optimization-based approach to parameter learning for fractional type nonlocal models	scientific article; zbMATH DE number 7546669

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instance of

scholarly article

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title

An optimization-based approach to parameter learning for fractional type nonlocal models (English)

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author

Yanyan Li

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publication date

23 June 2022

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full work available at URL

https://arxiv.org/abs/2010.03666

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zbMATH Keywords

identification problem

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optimal control

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nonlocal diffusion

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fractional Laplacian

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affine approximation

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describes a project that uses

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A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations

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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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Peridynamics and material interfaces

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A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators

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Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects

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A space-time fractional optimal control problem: analysis and discretization

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Optimal control of fractional semilinear PDEs

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Regularity analyses and approximation of nonlocal variational equality and inequality problems

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Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

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On a nonlocal Cahn–Hilliard model permitting sharp interfaces

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An energy-based coupling approach to nonlocal interface problems

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How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems

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Fractional diffusion on bounded domains

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Numerical methods for nonlocal and fractional models

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A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian

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The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator

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Identification of the diffusion parameter in nonlocal steady diffusion problems

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Bilevel parameter learning for nonlocal image denoising models

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A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints

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A FEM for an optimal control problem subject to the fractional Laplace equation

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Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

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Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

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Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

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Theory and practice of finite elements.

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The Dirichlet problem for nonlocal operators

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Optimizing the fractional power in a model with stochastic PDE constraints

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First Passage Times for Symmetric Stable Processes in Space

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Error Estimates for the Optimal Control of a Parabolic Fractional PDE

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Fractional Calculus: Integral and Differential Equations of Fractional Order

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

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Machine Learning of Space-Fractional Differential Equations

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A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation

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

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Numerical solution of the heat equation with nonlocal boundary conditions

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Analysis of a scalar nonlocal peridynamic model with a sign changing kernel

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On Fractional Laplacians

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Q5491447

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Sparse optimal control for fractional diffusion

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nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

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fPINNs: Fractional Physics-Informed Neural Networks

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Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization

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Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains

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A New Type of Identification Problems: Optimizing the Fractional Order in a Nonlocal Evolution Equation

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Is Gauss Quadrature Better than Clenshaw–Curtis?

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A spectral Galerkin approximation of optimal control problem governed by fractional advection-diffusion-reaction equations

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A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations

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A machine-learning framework for peridynamic material models with physical constraints

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Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions

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published in

Computers & Mathematics with Applications

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CAMWA.2021.05.005

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Sitelinks

Mathematics(1 entry)

mardi Publication:2147289