Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target contact laws, with only a few asperities in unit cells. The predicted designs are validated against high-fidelity Boundary Element Method (BEM) simulations. By front-loading computational costs during training, the neural surrogate yields near-instantaneous design inference, bypassing the bottlenecks of traditional multi-start optimization. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for the high-throughput discovery and real-time control of functional tribological surfaces.

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