A novel hybrid prediction approach for critical buckling strain of dented subsea pipelines coupling symbol regression and physics-informed neural networks

This study proposes a novel hybrid approach to predict the critical buckling strain (CBS) of dented subsea pipelines by coupling symbolic regression (SR) with physics-informed neural networks (PINNs). A 3D finite element model was developed to simulate pressurization, indentation, and longitudinal bending, alongside an improved far-field average strain method to stably capture CBS. Parametric analyses generated a database, enabling the development of an explicit, interpretable CBS prediction equation (R 2 = 0.968) via a Genetic Programming (GP-SR) algorithm. This equation was subsequently embedded into PINNs as a physical penalty, establishing the GP-SR-PINNs framework. Results indicate synergistic dent-bending causes severe W-shaped wrinkling. Deeper dents, larger diameters, and high-strength steels elevate buckling risks, whereas increased wall thickness and internal pressure enhance structural resistance; indenter size had negligible impact. Crucially, the GP-SR-PINNs framework boosted predictive accuracy to R 2 = 0.997. Beyond pure statistical precision, this physically-anchored network successfully extrapolated extreme damage conditions (20% dent depth) while restricting physics violation RMSE to 0.069. Furthermore, it maintained stable predictions under 10% measurement noise, overcoming the unphysical vulnerabilities of traditional black-box models to ensure reliable integrity evaluations in complex marine environments.