Latent space optimization for geometrically nonlinear topology via a condition-performance generative model

Topology optimization has fundamentally transformed structural conceptual design by enabling efficient and innovative material distribution. However, traditional methods encounter critical computational challenges under geometric nonlinearity, including prohibitive costs, high-dimensional design spaces and difficulties in enforcing global constraints. To address these issues, this study proposes a two-stage latent space optimization (LSO) framework based on a condition-performance variational autoencoder (CP-VAE). In the offline stage, CP-VAE learns a continuous low-dimensional latent manifold that jointly represents structural configurations, physical conditions, and nonlinear performance. In the online stage, the trained encoder, decoder and performance predictor are frozen, and the original density-based optimization is reformulated as a low-dimensional latent search problem, enabling rapid structure generation and performance evaluation without repeated nonlinear finite element analysis. The key methodological feature is a deep conditional injection mechanism that embeds physical conditions into multiple decoder layers, providing more persistent constraint control. A weighted multi-task training and sampling strategy is used to preserve latent diversity and performance awareness, while closed-loop re-encoding serves as a manifold consistency stabilization step during latent optimization. Experiments on a 2D cantilever beam problem demonstrate the proposed method achieves optimization quality comparable to SIMP in representative benchmark cases, with volume fraction errors within 2%, while reducing the online optimization time from hours to minutes after offline model training. A preliminary 3D geometrically nonlinear example is further tested to examine the scalability and generalization potential of the proposed framework. Beyond computational acceleration, the proposed framework contributes to engineering informatics by making condition-structure-performance relations in geometrically nonlinear topology design explicit, reusable, and searchable as a computational design representation, thereby enabling knowledge-guided design exploration and decision support.