Designing functional magnetic cloaks for real-world geometries

Magnetic cloaking enables objects to become undetectable to external magnetic fields while leaving those fields unperturbed. Existing demonstrations rely on idealized cylindrical or spherical shapes, limiting their practical relevance. Here, we introduce a physics-based optimization framework that designs magnetic cloaks for arbitrarily shaped structures by directly solving Maxwell's equations under spatial material constraints. Our method produces continuous, spatially varying permeability profiles that preserve field uniformity around complex geometries, including faceted and multi-lobed configurations. Using material parameters drawn from commercially available superconductors, we demonstrate low-distortion cloaking performance with permeability values within manufacturable ranges. This approach establishes a route to customizable magnetic shields for real-world components and lays the groundwork for future applications in extreme magnetic environments, such as fusion energy systems and precision instrumentation.