Physics-informed mechanical response prediction network of pipelines

Accurate condition evaluation for sewer pipeline is important. Existing data-driven neural networks rely heavily on large-scale labeled data and fail to incorporate inherent physical laws, leading to poor generalization under sparse data scenarios. Conventional physics-informed neural networks (PINNs) for elasticity, while overcoming data dependency, are limited to idealized geometric or material models and cannot capture pipeline-specific characteristics. To fill this gap, a physics-informed mechanical prediction method for sewer pipelines (PINN-SP) is proposed to embed domain-specific physical knowledges into the neural network. Integrating inspection, design, and operation data, the partial differential equations (PDEs) including physical information and damage geometric conditions are incorporated into the loss function. Four improvement methods are developed to address pipeline-specific challenges: non-dimensionalization to reduce training difficulty caused by disparate parameter magnitudes, a two-stage training strategy to avoid local extrema, the energy method to eliminate second-order differential terms in residual loss (enhancing computational efficiency and accuracy), and hard constraints to strictly enforce displacement boundary conditions. The accuracy of PINN-SP is verified against finite element simulation results. For both intact and damaged pipelines, the mean relative errors (MRE) of mechanical responses are less than 0.1, and the R² coefficients are higher than 0.9. This indicates that the proposed method can effectively fit physical PDEs, addresses the limitations of existing data-driven models and vanilla PINNs, and is suitable for engineering-oriented sewer pipeline mechanical response prediction.