Mass weighting algorithm optimizes Fourier-based physics-informed neural network in adhesive contact mechanics

Abstract

Physics-informed neural networks (PINNs) for elastic contact mechanics suffer from a spectral stiffness imbalance,that is, the elastic kernel grows linearly with wave number, causing short-wavelength modes to dominate gradient updates and stall convergence of the macroscopic deformation. We introduce a spectral preconditioning strategy that reweights displacement gradients in Fourier space before back-propagation, amplifying low wavenumber components through a mass weighting (MW) function while suppressing sub-grid noise via a built-in low-pass filter. Applied to adhesive line contact problems, the mass weighted PINN reaches machine-zero residual loss within 400 Adam iterations for specified benchmark, whereas the reference benchmark stalls at three orders of magnitude higher loss. The converged displacement and contact stress fields agree quantitatively with Green's function molecular dynamics (GFMD) solutions for both smooth Hertz contact at pressures spanning tension to compression and rough surfaces with roughness covering several decades of wavelength. The method operates directly on a uniform real-space grid, requires no explicit Green's function integration or quadrature rules, and is formulated entirely in terms of minimising a scalar energy function. Extension to two-dimensional rough surfaces is direct, as both the Fourier elastic energy and the spectral preconditioner depend only on the wave-number magnitude.