Fig. 1 General framework for predicting the repair effect of RPV steel with different pulse parameters

Fig. 2 Architecture of ANN model, consisted of one input layer, two hidden layers and one output layer

Fig. 3 Material aging with obvious Cu-rich clusters: a high angle annular dark field image; b energy disperse spectroscopy (EDS) detection results

Fig. 4 Ductile-brittle transition temperature value under various states: a the initial state; b aging for 400 °C-1000 h. After aging for 1000 h, the ductile-brittle transition temperature has changed from - 124.44 °C to - 93.62 °C, which meets the experimental requirements

Fig. 5 Spearman correlation coefficient matrix plot. Blue represents a positive correlation, and red represents a negative correlation; the * sign is a significant mark, which is set according to the change of the significance level, and it is displayed as *, ** and*** when it is less than 0.05, 0.01 and less than 0.001

Fig. 6 Quantity density estimates of original and generated datasets: a frequency; b duty ratio; c current; d time; e TTS. The distribution frequencies and fitting curves of the data in the original and generated are similar

Fig. 7 Taylor diagram comparing the performance of eight models. The scatter points represent the previously mentioned eight models, with the radial lines indicating R2, the horizontal and vertical axes representing MAE, and the dashed lines indicating RMSE. The PSO-RF model achieves maximum correlation at the closest distance to the reference point, making it the optimal model

Fig. 8 Comparison of some forecast results. The PSO-RF predicted value is closest to the true value

Fig. 9 Comparative results of the PSO-RF model performance

Fig. 10 Scatter plot of the predicted and actual values

Fig. 11 A bar chart for importance of different features

Fig. 12 Beeswarm plot of global SHAP analysis displays the impact of the inputs