Geometric continuity preservation in data-driven topology optimization via boundary-weighted eikonal loss and signed distance functions

Deep learning methods for topology optimization enable rapid design generation but frequently produce geometrically discontinuous structures unsuitable for manufacturing. This paper presents a mesh-independent framework that combines an implicit boundary representation based on signed distance functions (SDF) with a UNet–VAE generative model to address this fundamental limitation. The key contribution is a boundary-weighted eikonal loss that concentrates the gradient constraint ‖ ∇ f ‖ = 1 near structural boundaries, where geometric accuracy is most critical for maintaining material connectivity. Unlike uniform regularization, this targeted enforcement preserves thin members and eliminates spurious disconnections without compromising reconstruction fidelity. The framework comprises three components: (1) SDF-based shape representation ensuring smooth, continuous boundaries; (2) a UNet–VAE architecture with bilinear upsampling to eliminate checkerboard artifacts; and (3) the boundary-weighted eikonal loss for geometry-aware training. Numerical experiments on two benchmark datasets with simple and complex boundary conditions demonstrate that the proposed method reduces mean squared error by 80.9% and 91.2%, respectively, compared to baseline models, while maintaining structural similarity indices above 0.99. The generated structures preserve correct topology and connectivity patterns, enabling sub-second inference for physically valid designs applicable to engineering practice.