• An autoencoder-based deep learning framework reconstructs 3D solid–liquid two-phase flow in flexible vibrating pipelines using sparse wall sensor data.
• The X-model and F-model achieve high reconstruction accuracy with R2 values of 0.990 and 0.945, respectively.
• Optimal sensor configuration: 20 sensors (0.06% of total grids) provide a balance between accuracy and cost, with full-length arrangement outperforming front-end dense placement.
• The models demonstrate robustness across vibration parameters, physical fields, and vibration modes, with a signal-to-noise ratio tolerance of approximately 27 dB.