Physics-constrained two-stage reconstruction of contact pressure and real contact support in rough elastic contact

In rough tribological interfaces, the real contact area and local contact-pressure distribution are essential descriptors of asperity-scale load transfer and provide input fields for analyses of friction, wear, contact fatigue, and thermal or electrical contact resistance. Repeated high-resolution reconstruction of these fields from surface topography remains computationally demanding. This study proposes a physics-constrained two-stage deep-learning framework that separates latent pressure regression from contact-support prediction and combines the two outputs through hard gating. Hard gating enforces non-negative pressure and exactly zero pressure outside predicted support, while a Focal root-mean-square error (RMSE) loss emphasizes sparse high-pressure pixels. Separate load-specific models were trained at 30, 60, and 90 N. A controlled critic-on/off ablation at 256×256 and 30 N showed comparable reconstruction accuracy with and without adversarial training, indicating that the dominant performance gain arises from the two-stage formulation and hard gating rather than from the adversarial component itself. On synthetic RMD-generated rough-surface datasets, the model achieved a mean Dice score of 0.9909 and a mean pixel-wise accuracy of 0.9587; at 30 N, R_U² was 0.9995 and the p_99.9 relative error was 0.0049. Batch-1 end-to-end inference required 9.0 ms at  resolution on an NVIDIA RTX 3090 GPU. The predictions preserved prescribed load, contact-area trends, and dependence on RMS slope. An auxiliary test on axisymmetric oblate spheroidal profiles assessed smooth circular single-patch reconstruction, with the numerical fields checked against independent full-profile contact theory. On measured sandpaper-finished steel topographies without fine-tuning, mean Dice and coefficient of determination were 0.940 and 0.970 against FFT-BEM numerical references. Within the prescribed-load, frictionless linear-elastic regime, the framework provides a physics-constrained surrogate for rapid reconstruction of FFT-BEM-consistent contact-support and pressure fields.