A nonlocal physics-informed deep learning framework using the peridynamic differential operator

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the equation parameters. The performance of existing PINN approaches,...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-11, Vol.385, p.114012, Article 114012
Main Authors: Haghighat, Ehsan, Bekar, Ali Can, Madenci, Erdogan, Juanes, Ruben
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Computer architecture
Deep learning
Deformation
Elastoplasticity
Indentation
Machine learning
Neural networks
Numerical methods
Operators (mathematics)
Parameter identification
Partial differential equations
Performance degradation
Peridynamic Differential Operator
Physics
Physics-Informed Neural Networks
Solid mechanics
Surrogate models
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the equation parameters. The performance of existing PINN approaches, however, may degrade in the presence of sharp gradients, as a result of the inability of the network to capture the solution behavior globally. We posit that this shortcoming may be remedied by introducing long-range (nonlocal) interactions into the network’s input, in addition to the short-range (local) space and time variables. Following this ansatz, here we develop a nonlocal PINN approach using the Peridynamic Differential Operator (PDDO)—a numerical method which incorporates long-range interactions and removes spatial derivatives in the governing equations. Because the PDDO functions can be readily incorporated in the neural network architecture, the nonlocality does not degrade the performance of modern deep-learning algorithms. We apply nonlocal PDDO-PINN to the solution and identification of material parameters in solid mechanics and, specifically, to elastoplastic deformation in a domain subjected to indentation by a rigid punch, for which the mixed displacement–traction boundary condition leads to localized deformation and sharp gradients in the solution. We document the superior behavior of nonlocal PINN with respect to local PINN in both solution accuracy and parameter inference, illustrating its potential for simulation and discovery of partial differential equations whose solution develops sharp gradients. •A nonlocal physics-informed neural network using peridynamic differential operator.•A nonlocal architecture for caputing sharp gradients in the solution.•Parameter estimation of an elasto-plastic foundation loading problem.•Nonlocal architecture improves accuracy of solutions to forward and inverse problems.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114012