The modified physics-informed neural network (PINN) method for the thermoelastic wave propagation analysis based on the Moore-Gibson-Thompson theory in porous materials

This paper presents novel contributions to both theory and solution methodology in AI-based analysis of solid mechanics. The physics-informed neural network (PINN) method is developed for thermoelastic wave propagation and Moore-Gibson-Thompson (MGT) coupled thermoelasticity analysis of porous media, a first in the field. The coupled thermoelasticity governing equations, based on the MGT heat conduction model, are derived for a porous half-space, with the thermal relaxation coefficient and strain relaxation factor being considered. Mechanical and thermal shock loading boundary conditions are imposed. The behavior of a magnesium-made porous body is analyzed using the PINN method, with highly accurate results being achieved for the system of coupled PDEs. An adaptive hyperparameter tuning approach, integrating a generalized subset design (GSD) and Bayesian optimization algorithm, is used to automatically select the optimal structure based on the L2 relative error. This hybrid methodology eliminates manual adjustment concerns. The proposed method is verified through a thorough comparison with the Lord-Shulman theory of coupled thermoelasticity. The strength of the methodology lies in its ability to operate without domain data, with only boundary and initial points being required. Four example sets are examined to demonstrate the capabilities of the modified PINN, and high-quality predictions of dimensionless fields' variables over an extended time interval are obtained, confirming its extrapolation abilities.