A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity

08/16/2021
by   Mohammad Vahab, et al.
19

We explore an application of the Physics Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions to a few reference biharmonic problems of elasticity and elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that are challenging to solve using classical numerical methods, and have not been addressed using PINNs. Our work highlights a novel application of classical analytical methods to guide the construction of efficient neural networks with the minimal number of parameters that are very accurate and fast to evaluate. In particular, we find that enriching feature space using Airy stress functions can significantly improve the accuracy of PINN solutions for biharmonic PDEs.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 10

page 13

page 16

page 17

07/21/2019

Distributed physics informed neural network for data-efficient solution to partial differential equations

The physics informed neural network (PINN) is evolving as a viable metho...
02/14/2020

Optimally weighted loss functions for solving PDEs with Neural Networks

Recent works have shown that deep neural networks can be employed to sol...
02/06/2022

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems

Solving analytically intractable partial differential equations (PDEs) t...
07/09/2020

Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard...
04/11/2022

Improved Training of Physics-Informed Neural Networks with Model Ensembles

Learning the solution of partial differential equations (PDEs) with a ne...
10/06/2021

Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training

Physics-informed neural networks (PINNs) have received significant atten...
10/26/2021

Physics-Informed Neural Networks (PINNs) for Parameterized PDEs: A Metalearning Approach

Physics-informed neural networks (PINNs) as a means of discretizing part...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.