A Physics-Informed Design Generator for Long-Span Reticulated Domes: Replacing Iterative Finite Element Analysis for Optimal Solutions

The optimal design of long-span structures is hindered by the combination of prohibitively high computational costs and the limited physical consistency of purely data-driven surrogates. To address this challenge, this study proposes a multi-stage automated design framework that shifts the workflow from repeated per-task solving to reusable digital asset creation. First, a large-scale surrogate-optimized dataset containing 100,000 design samples is generated by embedding a high-speed MLP emulator into a Genetic Algorithm (GA). The core innovation lies in training a physics-regularized neural design generator. By incorporating a reduced-order total potential energy term derived from the principle of minimum potential energy as a regularization constraint, the network learns the mapping from external design conditions to validated near-optimal internal parameter combinations while suppressing mechanically unfavorable configurations associated with low stiffness. This mechanism improves mechanical admissibility, particularly in data-sparse regions. Validation results show that the generator achieves millisecond-level candidate generation and reduces the prediction error to 31% of that of conventional models under sparse-data conditions. In a like-for-like case study with identical external input parameters, the generated candidate design achieves a 21.1% reduction in total steel consumption. The proposed framework is therefore best understood as a rapid preliminary design tool for producing weight-efficient and mechanically admissible candidate schemes, which can then be subjected to subsequent high-fidelity analysis and code-based verification.