Fig. 1. Flow chart of the machine-learning system for designing the elemental anisotropy factor of CoCrFeMnNi HEA (a). An architecture of BPNN consisting of an input layer, two hidden layers, and one output layer (b).

Fig. 2. The electron backscatter diffraction (EBSD) inverse pole figure (IPF) map of the equiatomic CrMnFeCoNi HEA showing orientations of the loading axes of single-crystal micropillar (a), typical compressive stress-strain curves of single-crystal specimens with same grain and different positions at room temperature (b), and SEM images of the micropillars after the micro-compression tests (c-f).

Fig. 3. The tension model of HEA nano-pilar (a) and the HEA nano-pilar surface for 18 samples (b). Each element is distributed along the height direction (c). Radial distribution function of HEA (d).

Fig. 4. The atomic modeling of nano-pillar subjected to uniaxial tension, and stress vs. strain for different element distributions (a). Ultimate strength and elongation to failure (b).

Fig. 5. Deformation behavior of HEA nano-pillar with different chemical heterogeneities in samples A (a-c) and B (d-f). The surface topography and element distribution (a, d), microstructural evolution (b, e), and dislocation evolution (c, f). Dislocation-mechanism-dominated plastic deformation (a-c), and deformation-twinning-mechanism dominated plastic deformation (d-f).

Fig. 6. The elemental distribution of the HEA along the perimeter direction (a, b). The elemental anisotropy factor in samples A and B (c, d), where each pixel represents 1 × 1 nm2.

Fig. 7. Initial structure, intrinsic stacking fault, extrinsic stacking fault, and three-layer twin of HEA (a, b). The atoms of HEA are colored according to the atom type (a), and according to the CNA (b). Generalized stacking fault energy of the CoCrFeMnNi HEA (c). The ux stands for the moving distance along the special slip plane, where the blue arrows indicate different slip layers in (b). The initial structure corresponds to the moving distance of 0.0, the intrinsic stacking fault corresponds to the moving distance of 1.0, the extrinsic stacking fault corresponds to the moving distance of 2.0, and three-layer twin corresponds to the moving distance of 3.0.

Fig. 8. The MSE between predicted and target values in the training data, the validation data, testing data with the increase of the training epochs (a). The instances falling into different error ranges in the form of histogram (b).

Fig. 9. The predicted values from BPNN as the estimation function of the values from MD simulations for the training data, the validation data, the testing data, and all data.

Fig. 10. With the increased elemental anisotropy factor, the trade-off relationship between the ultimate strength (a) and elongation and the product of the ultimate strength and elongation (b). The comparison between CoCrFeMnNi HEAs with different elemental anisotropy factors, where red asterisk represent the optimal comprehensive performance (c).