Exploring the Capability of PINNs for Solving Material Identification Problems

Abstract

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving scientific and engineering problems that involve partial differential equations or physical constraints. PINNs are a type of neural network architecture that incorporates physical laws or governing equations into its learning process. By combining the strengths of deep learning and physics-based modeling, PINNs can learn complex patterns and relationships from data while simultaneously satisfying the governing equations or physical laws. In this work, we explore the capabilities of PINNs to solve physical problems and identify the material properties. The first validation example is 1D problem, in which the heat generation number is estimated in a rectangular fin with temperature dependant thermal conductivity and heat generation. The second example illustrates the behavior of a 2D linear-elastic beam subjected to a uniform traction at its tip, experiencing negligible strains and plane stresses. The goal in this example was to estimate the Young’s modulus. Finally, the third example studying here is a three-dimensional solid with a Neo-Hookean material, loaded with a compressive traction at the opposite end. In this case, the estimated parameters were the first and second Lame’s parameters. The reliability of the results was assessed comparing against the analytical solution of each case. The ground truth displacement data were obtained from analytical solution of the problem evaluated in selected data points. These values were used as input to evaluate the loss data function, while the remaining loss functions were derived from the physics of each problem. The results of this study suggest that PINNs have the potential to be an effective tool for both material identification problems and real-time prediction of the physical solution.