Attention-enhanced deep learning for stress-strain response prediction and inverse design of random porous materials

The mutual mapping between microstructures and material properties is fundamental to material design. To enable the inverse design of random porous materials with targeted stress-strain responses, this study introduces a latent space-driven, attention-enhanced deep learning framework. Nearly 20,000 random porous materials were generated through level-cut of Gaussian random fields, and their elastoplastic responses were simulated via finite element analysis. To reduce computational cost, the microstructure was projected into latent low-dimensional representational space using a variational autoencoder (VAE). Furthermore, based on the connotation of time consistency, the task of predicting stress-strain responses was reformulated as a temporal prediction problem, which was then addressed using a sequence transformer model based on the attention mechanism. Finally, a VAE2SeqT model was developed to map microstructure data to sequence-based representations. Additionally, an adaptive weight differential-enhanced loss function was proposed to capture the time-dependent nature of stress-strain curves. In the reverse process, a multi-objective optimization algorithm based on NSGA-III explores the Pareto optimal solutions closest to the target in the latent search domain, which are then mapped back to the original pixel space. The results demonstrate that latent space-driven deep learning frameworks perform well in both forward prediction and inverse design, offering promising pathways for the targeted design of complex materials in different fields.