A Physics-Guided Neural Network for Multioutput Prediction of Board-Level Thermal Process Parameters in Reflow Soldering

Abstract

Accurate prediction of board-level thermal process parameters is essential for reflow soldering process control, especially when experimental data are limited. This paper proposes a physics-guided neural network (PGNN) for multioutput prediction of key thermal process parameters in reflow soldering. The model uses conveyor speed, ten temperature zone settings, and cooling mode as process inputs, and simultaneously predicts preheat ramp rate, soak time, time above liquidus, peak temperature, and cooling rate. Process-level physical knowledge is incorporated into the training objective through soft regularization terms, including feasible thermal-parameter ranges and expected monotonic relationships between process settings and thermal responses. Bayesian optimization is further employed to tune the network architecture, training parameters, loss weights, and physical loss coefficient under cross-validation. Experimental results show that the optimized model achieves an average R2 value of 0.767 and an average mean absolute percentage error of 6.32% across the five prediction targets, with R2 values ranging from 0.667 to 0.874 and mean absolute percentage errors ranging from 0.82% to 8.78%. Compared with support vector regression, random forest, extreme gradient boosting, and a conventional artificial neural network, the proposed model provides competitive or improved overall performance for small-sample multioutput prediction. Shapley additive explanations analysis further identifies the key process factors for each target. The proposed framework provides a data efficient and interpretable tool for thermal-process evaluation and recipe optimization in reflow soldering.