Electromagnetic Sculptor: a differentiable geometric optimization framework to manipulate electromagnetic fields.

Electromagnetic fields are commonly controlled through geometric design, but existing approaches often lack efficient and differentiable modeling tools for complex shapes. Here we introduce Electromagnetic Sculptor, a differentiable geometric optimization framework for manipulating electromagnetic fields on arbitrarily meshed structures. The framework combines a numerical electromagnetic model based on shooting and bouncing rays with a gradient-based geometric optimizer that stabilizes mesh deformation through spatial filtering. To avoid excessive shape distortion during optimization, a shape-preserving regularization strategy is incorporated. The method is demonstrated using radar cross section reduction as a representative application. Numerical and experimental results show pronounced field suppression at both single frequencies and across a broadband range, while maintaining geometric smoothness and manufacturability. The framework enables fast optimization for models containing thousands of vertices, with simulated results consistent with experimental measurements. These results illustrate how differentiable computation can be integrated with physically grounded electromagnetic modeling and practical design constraints.