Efficiently Addressing Training Failures in 3D Elasticity Problems with PINNs

The use of Physics-Informed Neural Networks (PINNs) to solve linear elasticity problems has attracted significant research interest. However, in practical engineering applications, solving 3D linear elasticity problems with PINNs may sometimes fail. Our exploration into the reasons for these failures revealed that PINNs perform optimally within an ideal solution range. When output values fall within this range, PINNs are easier to train; outside this range, training becomes challenging. This work introduces a scaling method that enhances PINNs' ability to manage a wide range of solution scales in 3D linear elasticity problems. To further enhance convergence speed and robustness, an improved network architecture was introduced, validated on various 3D linear elasticity problems. This improved method effectively broadens the application capabilities of PINNs in practical engineering scenarios.