Tailoring the static friction of mechanical interfaces is critical for applications ranging from soft robotics to precision haptics. According to the Bowden and Tabor theory, static friction is governed by the real area of contact. However, for standard rough surfaces, this area grows linearly with load [1], severely restricting the range of achievable frictional behaviors. While recent approaches have proposed designing discrete spherical asperities to tune friction at specific operating points [2], or using generative diffusion models to reconstruct complex topographies [7], these methods often fail to control the constitutive response over a continuous loading range or lack physical interpretability. In this work, we extend the design space beyond standard spherical geometries to include general axisymmetric asperities [8], thereby unlocking a wider spectrum of mechanical responses. Following the recent success of physics-informed machine learning framework for the inverse design [3, 6], we introduce a hybrid Scientific Machine Learning (SciML) framework that embeds a differentiable analytical contact layer [4] for the forward problem and a 1D Convolutional Neural Network (CNN) for the inverse one. Unlike standard black-box surrogates, our model learns to map target Load-Area curves to interpretable topography parameters (asperity shape exponents and height offsets) by backpropagating physical gradients through the contact solver during training. This constraint allows the network to bypass the ill-posedness of the inverse problem by converging to a physically admissible “effective surface” that minimizes the error between the desired and achieved contact stiffness. We demonstrate that this approach successfully reproduces target constitutive laws that violate the fundamental Hertzian lower bound. The predicted topographies are verified against high-fidelity Boundary Element Method (BEM) simulations using the library Tamaas [5]. This framework establishes a scalable pathway for the automated discovery of tailored frictional surfaces, offering a robust tool for materials design, bridging the gap between fast surrogate modeling and rigorous contact mechanics.