On the Performance and Convergence of PINNs for Problems in Linear Elasticity

ABSTRACT Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations by embedding physical laws directly into the loss function. However, their performance characteristics for problems in computational mechanics remain insufficiently understood. This work presents a systematic investigation of PINN performance and convergence for three‐dimensional linear elasticity problems on a unit cube domain. Using the method of manufactured solutions, we study displacement fields of polynomial degrees one through four to assess how solution complexity affects convergence. We first examine the influence of collocation point distribution, studying the interplay between interior points enforcing equilibrium and surface points enforcing boundary conditions. We then investigate the effect of learning rate annealing on training convergence, followed by a study of network architecture depth and width, and finally the impact of Z ‐score input normalization. These techniques improve PINN performance and convergence, providing practical guidelines for configuring PINNs in computational mechanics applications.