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Physics-Informed Neural Network Approach for Surface Wave Propagation in Functionally Graded Magnetoelastic Layered Media

Diksha, Katyayani, Hriticka Dhiman, Soniya Chaudhary, Pawan Kumar Sharma, Mayank Kumar Jha

Abstract

This paper investigates propagation of SH-waves in a layered composite structure consisting of a pre-stressed functionally graded magnetoelastic orthotropic layer overlying a pre-stressed functionally graded orthotropic half-space under the influence of gravity. The study introduces a physics-informed neural network (PINN) framework for the dispersion analysis of SH-waves in the considered composite medium. As a benchmark, an analytical solution to the dispersion relation is derived and used to validate accuracy and reliability of the proposed PINN formulation. In the developed PINN model, the phase velocity corresponding to a prescribed wave number is treated as a trainable parameter, enabling the determination of the dispersion relation associated with the nonlinear eigenvalue problem. The Adam optimizer is employed to minimize the loss function during the training process. In addition, the effects of different activation functions and network architectures, including variations in number of hidden layers and neurons, are systematically investigated to study the performance of the proposed framework. Error analysis is carried out using several norms, namely $L_1$, $L_2$, RMSE, relative absolute error, and $L_\infty$, to assess the accuracy of the predictions. Furthermore, the variation of phase velocity with wave number under different material parameters is investigated. The comparison between the analytical and PINN-based results demonstrates excellent agreement, confirming the effectiveness of the proposed deep learning approach for analysing dispersion relations in complex layered composite structures.

Physics-Informed Neural Network Approach for Surface Wave Propagation in Functionally Graded Magnetoelastic Layered Media

Abstract

This paper investigates propagation of SH-waves in a layered composite structure consisting of a pre-stressed functionally graded magnetoelastic orthotropic layer overlying a pre-stressed functionally graded orthotropic half-space under the influence of gravity. The study introduces a physics-informed neural network (PINN) framework for the dispersion analysis of SH-waves in the considered composite medium. As a benchmark, an analytical solution to the dispersion relation is derived and used to validate accuracy and reliability of the proposed PINN formulation. In the developed PINN model, the phase velocity corresponding to a prescribed wave number is treated as a trainable parameter, enabling the determination of the dispersion relation associated with the nonlinear eigenvalue problem. The Adam optimizer is employed to minimize the loss function during the training process. In addition, the effects of different activation functions and network architectures, including variations in number of hidden layers and neurons, are systematically investigated to study the performance of the proposed framework. Error analysis is carried out using several norms, namely , , RMSE, relative absolute error, and , to assess the accuracy of the predictions. Furthermore, the variation of phase velocity with wave number under different material parameters is investigated. The comparison between the analytical and PINN-based results demonstrates excellent agreement, confirming the effectiveness of the proposed deep learning approach for analysing dispersion relations in complex layered composite structures.

Paper Structure

This paper contains 17 sections, 63 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Analytical Formulation
  3. Problem formulation
  4. Governing equation of motion and solution for the layer
  5. Governing equation of motion and solution for the half-space
  6. Boundary conditions
  7. Dispersion relation
  8. Physics-Informed Neural Networks for Dispersion Analysis
  9. Neural network approximation
  10. Physics loss function
  11. Extraction of the dispersion relation
  12. Neural network architecture
  13. Numerical Simulation and Graphical Representation
  14. Dispersion characteristics
  15. Validation of the PINN model
  16. ...and 2 more sections

Figures (11)

  • Figure 1: Schematic representation of the pre-stressed functionally graded layer–half-space composite medium
  • Figure 2: Schematic representation of the proposed PINN architecture for SH-wave dispersion analysis.
  • Figure 3: Dependence of normalized phase velocity on the dimensionless wavenumber $kH$ for different values of the heterogeneity parameter $\beta_i$ (a) in the layer and (b) in the half-space.
  • Figure 4: Dependence of normalized phase velocity on the dimensionless wavenumber $kH$ for different initial stress values in (a) the layer and (b) the half-space.
  • Figure 5: Dependence of normalized phase velocity on the dimensionless wavenumber $kH$ for different values of (a) Biot’s gravity parameter $(G)$ and (b) layer height $(H)$.
  • ...and 6 more figures