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

On the optimal control of a linear peridynamics model ⋮ Viscosity Solutions for Nonlocal Equations with Space-Dependent Operators ⋮ Error estimates for fractional semilinear optimal control on Lipschitz polytopes ⋮ An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator ⋮ On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models

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Identification of the diffusion parameter in nonlocal steady diffusion problems
The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel
Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
Optimizing the fractional power in a model with stochastic PDE constraints
Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization
Sparse optimal control for fractional diffusion
Numerical solution of the heat equation with nonlocal boundary conditions
Theory and practice of finite elements.
A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
A FEM for an optimal control problem subject to the fractional Laplace equation
Fractional diffusion on bounded domains
Bilevel parameter learning for nonlocal image denoising models
nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation
An energy-based coupling approach to nonlocal interface problems
A spectral Galerkin approximation of optimal control problem governed by fractional advection-diffusion-reaction equations
What is the fractional Laplacian? A comparative review with new results
A machine-learning framework for peridynamic material models with physical constraints
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
Regularity analyses and approximation of nonlocal variational equality and inequality problems
The Dirichlet problem for nonlocal operators
Peridynamics and material interfaces
Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains
How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
A Space-Time Fractional Optimal Control Problem: Analysis and Discretization
On Fractional Laplacians
A New Type of Identification Problems: Optimizing the Fractional Order in a Nonlocal Evolution Equation
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
First Passage Times for Symmetric Stable Processes in Space
A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
Error Estimates for the Optimal Control of a Parabolic Fractional PDE
On a nonlocal Cahn–Hilliard model permitting sharp interfaces
Optimal control of fractional semilinear PDEs
Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models
Fractional Calculus: Integral and Differential Equations of Fractional Order
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints
Machine Learning of Space-Fractional Differential Equations
fPINNs: Fractional Physics-Informed Neural Networks
A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
Is Gauss Quadrature Better than Clenshaw–Curtis?
Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations
Numerical methods for nonlocal and fractional models