Reproduce “A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity” on OpenResearch

About this paper

Josef Dick, Seungchan Ko, Quoc Thong Le Gia, Kassem Mustapha, Sanghyeon Park

Researchers introduce a decomposition-based Physics-Informed Neural Network (PINN) framework to robustly solve linear elasticity problems for materials in the nearly incompressible regime. This method effectively overcomes the "locking" phenomenon observed in standard PINNs by reformulating the governing equations, demonstrating superior accuracy and stability across various homogeneous and inhomogeneous material scenarios where conventional PINNs fail.

Key insights

• Standard PINNs fail in nearly incompressible regimes because the dominant, λ-dependent term in the loss function drives the solution towards a trivial (near-zero) state.
• Decomposing the problem into balanced subsystems effectively eliminates the extreme scaling imbalance, allowing the neural networks to learn the displacement fields accurately without locking.
• The framework's ability to learn intermediate functions like decomposed body forces and boundary conditions alongside field variables expands its utility for solving inverse problems.

Summary by alphaXiv.