Fig. 3: Metamaterial synthesis for four stress–strain responses not represented in the training dataset.
From: Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models
a–d, The model is conditioned on four technically relevant, challenging target responses, considering high stiffness in a, non-smooth stress increase in b, high compliance and drastic stiffness increase in c, and softening in d. Validation of the predicted effective stress response σeff (‘Fwd eval.’; NRMSE with respect to the target response in brackets) of the generated designs is achieved by FE simulations (‘FE eval.’), agreeing with the predicted response and substantially outperforming the best match in the training dataset (‘Best match’). We additionally compare the predicted full-field σ22 distribution (indicated in MPa in the Eulerian frame) with the FE ground truth and provide the corresponding relative L2 errors. To highlight the range of responses in the training dataset, we plot a representative selection in grey in a. aThe relative L2 error is numerically inflated due to the small magnitude of the stress field and is hence not truly indicative (but included for completeness).
