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

Area of Science:

• Computational mechanics
• Applied mathematics
• Neural network applications

Background:

• Elastodynamic problems require robust numerical methods for accurate simulation.
• Conventional physics-informed neural networks (PINNs) face challenges with stability and accuracy, especially with large time steps.

Purpose of the Study:

• Introduce a novel neural network architecture, Spectral Integrated Neural Networks (SINNs), for solving 2D and 3D elastodynamic problems.
• Enhance accuracy and stability in solving complex mechanical wave propagation problems.

Main Methods:

• Developed SINNs approximating second-order time derivatives of displacements via fully connected neural networks.
• Employed spectral integration to express displacements as linear combinations of these derivatives.
• Constructed a loss function incorporating equilibrium equations and boundary conditions using an improved numerical technique for accurate enforcement.

Main Results:

• SINNs demonstrate stability and high accuracy, even with large time steps.
• Computational experiments confirm the efficiency and reliability of the SINN framework.
• SINNs show superior accuracy and efficiency compared to conventional PINNs in numerical simulations.

Conclusions:

• SINNs provide a powerful and reliable framework for addressing elastodynamic problems.
• The proposed method offers significant advantages over existing neural network approaches for wave propagation analysis.
• SINNs represent a promising advancement in computational mechanics for simulating dynamic systems.