Memory-Augmented Conditional GAN for Continuous Mechanical Response Field Generation

Generating continuous mechanical response fields under small-sample conditions remains a critical challenge in civil engineering. This paper proposes MMA-CGAN, a memory-augmented multi-head attention conditional generative adversarial network. A learnable external memory matrix is embedded into its multi-head attention module to store and retrieve global prior mechanical patterns, thereby compensating for weak feature representation under sparse samples. Its effectiveness is validated on two representative datasets: a homogeneous rectangular thin plate under localized patch loading and a multi-layered soil mass under a concrete column. Under interpolation validation within the training parameter ranges, on the thin-plate dataset, MMA-CGAN achieves R2 no lower than 0.997 for strain, stress, and displacement predictions, substantially outperforming XGBoost and Random Forest while attaining accuracy comparable to a well-tuned multilayer perceptron (MLP), with the additional generative data-augmentation capability unavailable to pure regression models. On the soil dataset, its advantage widens as the parameter space expands. Under single-load variation, MMA-CGAN performs comparably to MLP. Under simultaneous variation of load and elastic modulus, its mean squared error (MSE) is approximately one order of magnitude lower than that of MLP. Under the three-variable coupling of load, elastic modulus, and cohesion, MMA-CGAN maintains R2=0.999, whereas MLP drops to 0.985. Ablation studies confirm the critical role of the memory module: its removal degrades MSE by approximately 13-fold and 4.5-fold in the single-variable and three-variable cases, respectively, indicating that the memory module and multi-head attention operate synergistically rather than as a simple cascade. For high-degree-of-freedom application scenarios lacking explicit empirical constraints such as governing equations, the proposed MMA-CGAN achieves high-fidelity data augmentation via implicit distribution learning, providing a feasible pathway to overcome the bottleneck of scarce experimental samples in complex structural analysis within the trained parameter space.