A Combination of Deep Neural Networks and Physics to Solve the Inverse Problem of Burger's Equation

Shaikhah Alkhadhr, Mohamed Almekkawy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

One of the most basic nonlinear Partial Differential Equations (PDEs) to model the effects of propagation and diffusion is Burger's equation. This puts great emphasize on seeking efficient versatile methods for finding a solution to the forward and inverse problems of this equation. The focus of this paper is to introduce a method for solving the inverse problem of Burger's equation using neural networks. With recent advances in the area of deep learning, a Physics-Informed Neural Network (PINN) is a category of neural networks that proved efficient for handling PDEs. In our work, the 1D and 2D Burger's equations are simulated by applying a PINN to a set of domain points. The training process of PINNs is governed by the PDE formula, the initial conditions (ICs), the Boundary Conditions (BCs), and the loss minimization algorithm. After training the network to predict the coefficients of the nonlinear PDE, the inverse problem of the 1D and 2D Burger's equations are solved with an error as low as 0.047 and 0.2 for 1D and 2D case studies, respectively. The wave propagation model is accomplished with an approximate training loss value of 1×e -4 . The utilization of PINNs for modeling Burger's equation is a mesh-free approach that competes with the commonly used numerical methods as it overcomes the curse of dimensionality. Training the PINN model to predict the propagation and diffusion effects can also be generalized to address further detailed applications of Burger's equation with complex domains. This contributes to clinical applications such as ultrasound therapeutics.

Original languageEnglish (US)
Title of host publication43rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4465-4468
Number of pages4
ISBN (Electronic)9781728111797
DOIs
StatePublished - 2021
Event43rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2021 - Virtual, Online, Mexico
Duration: Nov 1 2021Nov 5 2021

Publication series

NameProceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS
ISSN (Print)1557-170X

Conference

Conference43rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2021
Country/TerritoryMexico
CityVirtual, Online
Period11/1/2111/5/21

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Biomedical Engineering
  • Computer Vision and Pattern Recognition
  • Health Informatics

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