Inverse design of architectural floorplans with gradient-based optimization of binary subdivision graphs

Computer-aided floorplan synthesis automates a core task in architecture and construction planning: balancing room programs, connectivity, areas, and boundary constraints. The fuzzy nature of machine-learning models makes it difficult for generative methods to achieve the precision and predictable edits needed in architectural design. Building on a hypergraph representation coupling binary subdivision graphs with access graphs, this paper proposes a gradient-based inverse-design workflow for controllable floorplan synthesis. Its differentiable soft-split formulation converts subdivision parameters into continuous room masks, allowing room areas and compactness to be optimized while preserving a prescribed or retrieved subdivision structure. Compared with non-differentiable optimization, this method is faster and performs favorably on several connectivity metrics. Residential floorplan experiments show improved access satisfaction and area accuracy over existing methods. The effectiveness of the proposed method is demonstrated across several design scenarios, supporting interactive computer-aided design and controllable layout synthesis for early-stage decision making under varied design requirements.