Performance-based inverse design of nonlinear mechanical metamaterials via enhanced conditional generative adversarial networks

A shift is occurring from avoiding structural geometric nonlinearities to deliberately exploiting them for new functionalities. Forward design–predicting nonlinear responses from given parameters–is well established, but the inverse problem–identifying parameters that yield a desired nonlinear behaviour–remains a major challenge due to the complexity of the response. Developing an efficient inverse design framework is therefore essential to enable broader application of nonlinear mechanical metamaterials. To address this, we introduce an enhanced conditional generative adversarial network (c-GAN) framework that synergizes three key innovations: (i) surrogate-based physics-informed supervision via a pre-trained simulator network, (ii) residual generator architecture for stable gradient flow, and (iii) structured noise encoding for enhanced diversity and controllability. This c-GAN-Physics-Stochastic architecture generates precise geometric parameters in a single forward pass, bypassing traditional iterative optimization bottlenecks. We demonstrate the framework’s effectiveness through two case studies: mechanical metamaterials designed for recoverable energy dissipation via sequential snap-through instabilities, and auxetic metamaterials maintaining a constant Poisson’s ratio under large deformations. Experimental results validate the physical realisability of the generated designs. Inference with the conditional GAN provides millisecond-level design prediction, while a hybrid c-GAN + genetic algorithm (GA) refinement strategy achieves exceptional agreement with high-fidelity evaluations (up to R 2 > 0.99 ) at increased computational cost. This work demonstrates the potential of data-driven methods, particularly c-GANs, in addressing the inverse design challenge for nonlinear mechanical metamaterials for novel functionalities. By delivering an accessible toolbox, we aim to promote its widespread use and practical implementation by engineers, paving the way for innovative applications.