Simultaneous Topology Optimization of Differentiable and Non‐Differentiable Objectives via Morphology Learning: Stiffness and Cell Growth on Scaffold

Topology optimization (TO) of microstructures plays a critical role in optimizing functional performance across diverse engineering applications. While metamaterials with enhanced mechanical properties—such as hyperelasticity, energy absorption, and thermal efficiency—are commonly designed using complex microstructural geometries and multi‐physics simulations, achieving the simultaneous optimization of mechanical performance and non‐differentiable objectives remains a significant challenge. In this work, a novel framework is proposed for simultaneous TO of differentiable and non‐differentiable objectives via a data‐driven morphology learning approach. The framework extracts shape patterns from a curated dataset of microstructures recognized for their superior performance in specific functional applications. To showcase the versatility of the approach, it is applied to the optimization of scaffolds for bone tissue engineering, with cell growth as a representative functional objective. By integrating learned morphology patterns into a TO process, the method generates microstructures that effectively balance mechanical stiffness and biological performance, such as enhanced cell proliferation. As a case study, a scaffold design that improves mechanical stiffness by 29.69% and cell growth by 37.05% on day 7 and 33.30% on day 14 is demonstrated. This approach highlights the general applicability of the proposed framework for optimizing a broad range of engineering challenges, beyond the specific case of cell growth.