Fig. 2: Inverse design of buckling-resistant lattice materials.

a Schematic information flow during property (buckling strength) prediction using DNN. b Example of predicted vs. target (ground truth) property of a generic non-uniform 4 × 4 unit cell. Lines are plotted only to facilitate the interpretation. c Dataset used for training and testing the DNN. d Predicted vs. target fitness values for the whole dataset and for 12 inverse-designed architectures. e Best 6 design candidates output by the inverse-design algorithm. f Simulated post-buckled shape of the first best design candidate loaded at θ = 0°. PBCs are imposed on a 10 × 10 super-cell. g Simulated stress-strain curves of the first design candidate and sponge-inspired designs at five different loading angles. h Normalized effective buckling strength of the first design candidate at different loading directions compared to that of the sponge-inspired designs. Lines are plotted only to facilitate the interpretation. To compare the DNN predictions with the FE-simulated values, in g and h a single unit cell with PBCs is considered; a slight decrease in performance is exhibited due to global buckling effects, as shown in Supplementary Fig. 8.