Comparative analysis of standard PINN and gradient-enhanced PINN approaches for thin plate bending problems

This paper introduces a novel gradient-enhanced physics-informed neural network (gPINN) framework for analyzing Kirchhoff-Love plate bending under diverse boundary conditions. The approach marks a significant advancement in physics-informed machine learning by offering three key innovations: (1) a gradient-regularized loss function that enforces the biharmonic equation and boundary constraints concurrently; (2) a modular neural architecture featuring interconnected subnets for transverse and in-plane displacements; (3) an adaptive training algorithm with physics-informed sampling strategies. The proposed technical framework integrates several pioneering elements. It augments the strain energy functional with higher-order gradient terms to accurately capture curvature effects near plate boundaries. Furthermore, it introduces edge-specific penalty functions that automatically accommodate various support conditions, such as clamped, simply supported, and free edges, without requiring geometric remeshing. The network design further integrates dedicated submodules for displacement gradients, utilizing shared weights for mixed partial derivatives critical to the bending moment formulation. Numerical validations across three benchmark cases (complex boundary conditions) highlight the framework’s superiority over traditional PINNs. Notable outcomes include: (I) a 72% average reduction in relative error at boundary transitions (p < 0.01); (II) convergence to engineering accuracy (<% error) in 38% fewer iterations; (III) robust generalization to untested boundary condition combinations. The gPINN solutions align closely with finite element benchmarks while eliminating meshing dependencies, demonstrating particular strength in high-stress concentration zones. This study sets a new benchmark for physics-informed deep learning in plate mechanics, offering immediate relevance for designing aerospace components, marine structures, and other thin-walled structures where precise deformation prediction under complex constraints is essential. The gradient enhancement methodology provides a scalable blueprint for applying physics-aware machine learning to other fourth-order boundary value problems in solid mechanics.