Fig. 4: DFT validations.

a Distributions of deviations for 100 random samples from the X-Mn-O dataset, measured using MAE in coordinates (Å) between the unrelaxed and DFT-relaxed structures. b Energy distribution for the three types of structures among the 100 random samples from the X-Mn-O dataset. The boxplots show the median (black line inside the box), interquartile range (box), and whiskers extending to 1.5 times the interquartile range, with outliers plotted as individual points. c Distribution of deviations for 100 random samples from the Materials Project dataset with relatively rational initial structures. d Energy distribution for the three types of structures among the 100 random samples from the Materials Project dataset. e Distributions of deviations for 20 random samples from the 2D materials defect dataset. f The number of DFT ionic steps required to complete DFT structure relaxation, starting from the initial unrelaxed structures and the DeepRelax-predicted structures, respectively. The samples are sorted based on the number of ionic steps required by the unrelaxed structures for better observation. Source data are provided in this paper.