Cellular topology optimization on differentiable Voronoi diagrams

Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated lies devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete structure, e.g., a Voronoi diagram, whose relies on cells faces, lacks its differentiability facilitate large-scale, gradient-based topology optimizations. We propose optimization algorithm based differentiable generalized that can evolve structure as continuous field. The central piece of our method is hybrid particle-grid encode previously diagram into density field defined Euclidean space. Based this representation, we further extend it tackle anisotropic cells, free boundaries, functionally-graded structures. Our enables integration state-of-the-art pipelines, which defines novel design space explore options effectively were impractical previous approaches. showcase efficacy approach with up thousands including femur bone Odonata wing.