A Decomposition-Based Robust Training of Physics-Informed Neural Networks for Nearly Incompressible Linear Elasticity

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity deteriorates as the Lamé coefficient [Formula: see text], or equivalently as the Poisson ratio [Formula: see text]. While this locking phenomenon is well known in classical numerical methods, its impact on physics-informed neural networks (PINNs) has not been systematically studied. We show that standard PINNs also suffer from a form of locking (PINN locking) in the nearly incompressible regime, leading to severe degradation in approximation quality and optimization performance. Our main contribution is a decomposition-based PINN formulation that rewrites the elasticity equations into balanced subsystems, yielding a PINN locking-robust training framework whose performance does not deteriorate with large [Formula: see text]. The framework applies to both forward and inverse problems and accommodates constant, variable, and parametric Lamé coefficients. We further perform a priori error analysis for the proposed formulation. Numerical experiments demonstrate consistent and substantial improvements over standard PINNs in both solution accuracy and parameter recovery across a wide range of nearly incompressible settings. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/Sanghyeon-Park99/decomposition and in the supplementary materials ( decomposition-main.zip [733KB]). [Formula: see text]