Dimension-reduced physical-informed neural network for temperature field of thin-walled dumbbell-shaped steel tube under solar radiation

For transient heat conduction in dumbbell-shaped thin-walled steel tube cross-sections under solar irradiation, conventional two-dimensional physics-informed neural networks (PINNs) are prone to residuals dominated by stiff radial terms when the wall-thickness and circumferential scales are widely separated and the coordinates are normalized simultaneously, leading to a decoupling between loss convergence and solution accuracy. To address this issue, a thin-walled PINN framework under solar radiation (Solar-tPINN) that features dimensionality reduction and domain decomposition is proposed. Based on the thin-walled assumption, the radial-circumferential heat conduction is reduced to a one-dimensional transient circumferential equation, thereby removing from the governing equation the radial degrees of freedom responsible for residual scale separation. Meanwhile, inspired by the extended PINN domain decomposition strategy, the domain is partitioned at geometric discontinuities, and the resulting subdomains are connected by temperature continuity and energy balance conditions. The results show that the maximum error of the reconstructed temperature field obtained by Solar-tPINN is less than 1.50 °C, while its root mean square error and symmetric mean absolute percentage error are 0.53 °C and 1.49%, respectively, both substantially lower than those of the improved 2D PINN (5.39 °C and 9.30%). Good temperature continuity and energy balance are maintained at the tube-web junctions. In thermal conductivity inversion, although standard 2D and coefficient rescaling 2D PINNs achieve loss convergence, the results exhibit pronounced parameter distortion and oscillatory overshoot followed by decay, respectively. In contrast, Solar-tPINN achieves stable converged, with an identification error of only 0.36% for the circular steel tube case. When further extended to dumbbell-shaped cross-sections with multiple subdomain couplings, the relative error remains below 6.85% under synthetic measurement noise. Ablation and sensitivity analyses further demonstrated the necessity of domain decomposition at geometric discontinuities and the robustness of Solar-tPINN to perturbations in loss weights. The proposed method provides an effective physics-informed framework for reconstructing solar-induced temperature fields and identifying thermal properties in complex thin-walled structures with large aspect ratios