nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
type: Item
instance of: scholarly article
title: nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
author: Marta D'Elia
author: Michael L. Parks
author: Guofei Pang
author: George Em Karniadakis
published in: Journal of Computational Physics
publication date: 2022-04-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/2004.04276
Mathematics Subject Classification ID: 35-XX
Mathematics Subject Classification ID: 86-XX
zbMATH DE Number: 7508384
zbMATH Keywords: nonlocal models
zbMATH Keywords: deep learning
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: physics-informed neural networks
zbMATH Keywords: turbulence modeling
describes a project that uses: Adam
describes a project that uses: FPINNs
MaRDI profile type: Publication
OpenAlex ID: W3048778144
cites work: Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
cites work: Optimal control of fractional semilinear PDEs
cites work: Continuous and discontinuous finite element methods for a peridynamics model of mechanics
cites work: Fractional diffusion on bounded domains
cites work: Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes
cites work: A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
cites work: The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
cites work: Identification of the diffusion parameter in nonlocal steady diffusion problems
cites work: Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
cites work: A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
cites work: Q3091364
cites work: Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
cites work: fPINNs: Fractional Physics-Informed Neural Networks
cites work: Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization
cites work: Hidden physics models: machine learning of nonlinear partial differential equations
cites work: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
cites work: Tempered fractional calculus
cites work: Reformulation of elasticity theory for discontinuities and long-range forces
cites work: Peridynamic modeling of membranes and fibers
cites work: Deformation of a peridynamic bar
cites work: On the distribution of points in a cube and the approximate evaluation of integrals
cites work: STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION
cites work: A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives
cites work: Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
DOI: 10.1016/J.JCP.2020.109760
description: scientific article; zbMATH DE number 7508384