A nonlocal physics-informed deep learning framework using the peridynamic differential operator
Name
2006.00446.pdf
Description
Submitted version
Size
5.95 MB
Format
Adobe PDF
Checksum (MD5)
38e9c4b4133cefacdb52db12cd94bca9
Author(s)
Haghighat, Ehsan
Bekar, Ali Can
Madenci, Erdogan
Juanes, Ruben
Date Issued
July 2021
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Citation
Ehsan Haghighat, Ali Can Bekar, Erdogan Madenci, Ruben Juanes, A nonlocal physics-informed deep learning framework using the peridynamic differential operator, Computer Methods in Applied Mechanics and Engineering, Volume 385, 2021
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.cma.2021.114012
