Real-time reconstruction of the internal temperature field of welding using global physics-mixed long short-term memory network and physical constraint reconstruction

Accurate reconstruction of internal welding temperature fields is essential for evaluating thermal cycles and weld quality, yet direct internal measurement is difficult. This study proposes a real-time reconstruction framework for the internal temperature field of SUS304 gas metal arc welding (GMAW) butt joints by coupling a physics-constrained mixed deep operator network (PMix-DeepONet) predictor with spatio-temporal physics-augmented plate spline interpolation (ST-PAS). In PMix-DeepONet, a global physics-mixed long short-term memory (Mix-LSTM) encoder performs physical mixing of welding current, voltage, surface molten-pool temperature, and temporal information before recurrent encoding, enabling the branch network to capture multi-source process dynamics. The DeepONet branch-trunk operator-learning structure then maps the encoded process features and spatiotemporal coordinates to the internal temperature field, while heat-transfer, boundary-condition, initial-condition, and high-temperature-sensitive constraints guide the prediction toward physically meaningful solutions. ST-PAS further combines an adaptively fitted Goldak-like thermal-shape prior with residual plate-spline correction to refine sparse reconstructed fields while preserving nonlinear heat-field morphology. Experiments show that PMix-DeepONet reduces the overall root mean square error (RMSE) from 35.78 °C to 22.09 °C compared with DeepONet. In the high-temperature region above 1000 °C, the RMSE decreases from 66.78 °C to 23.71 °C. Ablation results confirm the importance of Mix-LSTM and physical constraints for stable high-gradient prediction. For spatial refinement, ST-PAS achieves the lowest RMSE of 57.90 °C and MSE of 3352.05, reducing RMSE and MSE by 1.09% and 2.18% compared with LSM-SP. Qualitative comparisons further verify the effectiveness of the framework for real-time SUS304 GMAW temperature-field prediction.