Abstract: This study proposes a complete technical chain from precise mechanical modeling to efficient optimization for the out-of-plane stability issue of arch structures. The 14×14 exact matrix stiffness method (MSM) considering warping deformation is employed to solve the out-of-plane buckling load and establish a high-fidelity dataset. An artificial neural network (ANN) integrated with attention mechanism and residual connections is trained to predict the buckling capacity rapidly (R²>0.98 on the test set). SHAP analysis reveals that the lateral bending stiffness of arch rib and brace positions are the most critical factors. On this basis, under the material volume constraint, an ANN surrogate model-driven gradient descent constrained optimization framework is developed. Case study results show that for five symmetrically distributed braces, the optimal positions are 0.1660S and 0.3180S with k=1.27, achieving a non-dimensional critical buckling load of 29.12. Compared with traditional empirical equal-spacing bracing arrangement and the weak-bracing S/4 reference scheme proposed by Pan et al., the present optimization scheme increases the out-of-plane critical buckling load by 42.6% and 38.2%, respectively, while maintaining the same total steel volume. Compared with traditional genetic algorithm (GA) and article swarm optimization (PSO), the computational efficiency is improved by approximately 400 times with significantly better convergence stability. This study provides an efficient and accurate technical approach for the intelligent optimization design of out-of-plane stability bracing systems in arch structures.