PSI - Issue 68

1034 Giuseppe Bonfanti et al. / Procedia Structural Integrity 68 (2025) 1031–1037 G. Bonfanti et al. / Structural Integrity Procedia 00 (2025) 000–000 j connected by the strut; Similarly, 58 = 5 − 8 is the distance in y direction; CD 58 DC = H 58 9 + 58 9 is the euclidian norm of distance vectors; 5 #" = ;< 7 = : $% <; is the axial stiffness where E is the Young’s modulus and A the area of strut profile; 5 $ = ;<= 7> $% <; is the bending stiffness where I is the moment of inertia. The FE results—nodal displacement, reaction forces, effective stiffness, effective strength and effective Poisson’s ratio—were embedded in an output vector. The edge feature, node feature and ground truth values were normalized using StandardScaler function from the sklearn library. The first layer of the multi-head attention mechanism was stabilized using concatenation, while the others GAT layers were performed by averaging because of the loss of sensibility of the GAT final layer (Veličković, Cucurull et al. 2017). The final layer was composed of a pooling layer—global mean pool that returns batch-wise graph-level outputs by averaging node features across the node dimension. To train this networks, Mean Absolute Error (MAE) = 0 ? ∑ | 5 − L 5 | 0 5@? was employed as loss function. The Adam optimizer was used with an initial rate of 0.001 for the model predicting effective stiffness and effective Poisson’s ratio and 0.0009 for the model predicting the effective strength, respectively. Moreover, the exponential decay of the Adam optimizer was kept as 0.95 every epoch for above three models. L2 regularization was adopted to reduce overfitting with a 1 x 10 AB weight decay of the prediction of the effective stiffness and effective Poisson’s ratio and 2 x 10 AB weight decay for the prediction of the effective strength, respectively. Mini-batching was also employed on training and validation dataset. The total number of data was 10000 and the database was split as follows: 60% of training data, 20% of validation

data, and 20% of testing data. 2.3. Inverse Design Algorithm

GA—an algorithm is inspired by biological evolution process (Michalewicz and Schoenauer 1996)—is designed to solve problems with multiple solutions and complex search spaces. Inspired by our work (Maurizi, Gao et al. 2022), we developed the inverse design of nonuniform lattice structure by integrating GA as shown in Fig. 2.

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Figure 2 The schematics of inverse design algorithm

The algorithm was run 10 times for each category goal, and GNN’s predictions were validated by evaluating the best final designs through FE simulations. The detailed steps to build inverse design algorithm were described as follows. 1) The random.sample function from the Python random is employed to select an initial population of 100 individuals. This function returns a list of items randomly chosen from the sequence.