Prediction of Mechanical Properties and Inverse Design of Columns with Complex Cross-Sections Based on Deep Learning Methods

Solid-web steel-reinforced concrete (SRC) columns are widely utilised in building structures. Currently, the design of complex cross-sectional columns (CCSCs) primarily relies on finite-element models (FEM) or empirical formulas. Both routes, however, carry penalties: empirical and semi-empirical models lack accuracy and flexibility for arbitrary cross-sections, whereas finite-element simulation of such geometries demands considerable modelling effort and is inefficient. This study introduces a CCSC design framework that directly predicts the mechanical performance of columns based on cross-sections. It employs the displacement–force relationship as a constraint to inversely design cross-sectional forms that can meet specified demands. The framework learns the conditional distribution of cross-sectional forms for given mechanical properties, enabling a reversible, one-to-many geometry-to-performance mapping. Consequently, this work can simplify and accelerate the design of structural components with complex target performances. Results show that the Vision Transformer (ViT) reduces the mean squared error (MSE) by 62.72% relative to ResNet18 (mean absolute percentage error (MAPE) 12.95% versus 30.20%). In the inverse design, generated sections attain a root mean square error (RMSE) of 5.99 kN, and the diffusion exponential-integrator sampler (DEIS) reaches the target in 10 steps, about 1% of the 1000 denoising diffusion probabilistic model (DDPM) steps, while preserving accuracy.