Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems

Spectral integrated neural networks with large time steps for 2D and 3D transient elastodynamic analysis

This paper provides a neural network architecture, called spectral integrated neural networks (SINNs), designed to tackle two- and three-dimensional elastodynamic problems. In the SINNs, the second-order time derivatives of displacements are approximated through the adoption of a fully connected neural network. Subsequently, the displacements are expressed as linear combinations of the second-order time derivatives of displacements using the spectral integration. Finally, the loss function is derived by incorporating the displacements into the elastic equilibrium equations and the boundary conditions. An improved numerical technique is employed in the construction of the loss function to accurately enforce the boundary conditions. The primary strength of the present SINNs lies in its ability to maintain both stability and high accuracy, even when utilizing large time steps. A series of computational experiments validates the efficiency and reliability of the proposed framework. The numerical results demonstrate that the SINNs exhibit enhanced accuracy and efficiency compared to conventional physics-informed neural networks (PINNs).