Solving Layered Rough Contact via a Physics-Informed Operator Framework

Predicting three-dimensional layered rough surface contact behavior is fundamental to modern tribological interface design and surface engineering. However, experimental measurements lack sub-surface resolution, theoretical models rely on oversimplified geometric assumptions, and high-fidelity numerical methods remain computationally prohibitive for multiscale interface problems. To address these limitations, we develop a physics-informed operator-decomposition framework that separates the unknown nonlinear contact-state mapping from the analytically known elastic compliance operator. This framework combines an attention-enhanced U-Net with a Fourier Neural Operator (FNO) to capture localized and long-range interactions while decomposing the predicted surface deformation into elastic and plastic components. By incorporating penalty terms derived from the Karush-Kuhn-Tucker (KKT) contact conditions into the loss function, the framework promotes physically admissible predictions with respect to nonpenetration, pressure nonnegativity, and contact complementarity. Furthermore, a multiscale feature-wise linear modulation (FiLM) module dynamically injects dimensionless physical parameters into the convolutional feature maps, facilitating generalization across broad ranges of coating properties and system scales. Validation against standard boundary element method (BEM) calculations demonstrates that the framework achieves high fidelity across diverse topographies while reducing full-field inference times from minutes to milliseconds. Overall, the proposed framework provides an efficient and physically interpretable surrogate for resolving full-field pressure and displacement responses in layered rough contact across broad geometric, material, and loading regimes.