An end-to-end and high accuracy solution of cable catenary using dual-parameter optimized physics-informed neural networks

Cable-stayed bridges are complex structures requiring precise determination of cable shape parameters for design, analysis, and construction management. With increasing bridge spans, geometric nonlinearities complicate the resolution of catenary equations. Traditional methods demand high expertise and involve intricate calculations, creating barriers to practical implementation. This study introduces a Cable-Catenary Physics-Informed Neural Network (CC-PINN) as an end-to-end, high-precision method for solving cable catenary problems. The proposed approach features a dual-parameter optimization strategy that simultaneously updates neural network parameters and catenary characteristic angle parameters with different learning rates, addressing unique challenges in cable modelling. Numerical experiments compare CC-PINN with traditional Newton and Secant methods across various cable configurations. Results demonstrate that CC-PINN achieves higher terminal accuracy than Newton's method and matches the precision of the Secant method at boundary conditions. Statistical analysis confirms no significant differences in characteristic angle calculations between CC-PINN and traditional approaches. Analysis shows a learning rate of 0.01 for angle parameters achieves optimal performance, balancing stability and convergence speed—especially for longer cables, where efficiency improves by up to 54.9%.By lowering technical barriers while maintaining analytical rigor, CC-PINN enables broader application of advanced modeling techniques in practical bridge engineering, contributing to more efficient design and construction of cable-stayed bridges.