Designing hyperelastic porous microstructures under finite strain is challenging because bending, buckling, contact, and densification interact to produce nonconvex and one-to-many relationships between topology and response. We present HyperDiff, a conditional diffusion framework that reformulates inverse design as probabilistic sampling rather than deterministic regression. A compact B-spline encoding of the target force--displacement curve captures the system's energy-evolution trend and provides temporal and mechanical context that guides denoising toward physically consistent configurations with the desired multistage deformation behavior. The workflow integrates Gaussian random field (GRF)-based topology generation, constitutive calibration, large-deformation finite-element simulations, and quasi-static compression experiments. Across held-out and interpolated targets, the generated microstructures accurately reproduce sequential deformation stages and global responses, with deviations typically below 10%, while preserving manufacturability and one-to-many design diversity. The current implementation focuses on two-dimensional unit cells under quasi-static compression. However, the framework is extensible to 3D, multiresolution, and multiphysics systems. By combining physics-aware conditioning with generative sampling, HyperDiff provides a practical front end for mechanics-based design workflows, including the design of programmable soft actuators and impact-energy absorbers with tunable plateaus, as well as the rapid exploration of nonlinear architected materials for soft and deformable systems.

Learning reusable local operators can accelerate thermoelastic topology optimization, yet accurate stiffness prediction alone does not ensure accurate thermal-force transfer between fields. A hybrid Problem-Independent Machine Learning (PIML) framework combines reference-anchored thermal shape-function learning with mechanical residual-enriched static condensation. A fixed-trace error analysis exposes the mechanism: stiffness errors are quadratic about interior equilibrium, whereas thermal-load projection can retain first-order errors. This distinction motivates a field-specific strategy that learns the compact thermal response and corrects the larger mechanical response from current-material equilibrium. Shared Ritz factors supply stiffness, coupling and local state/adjoint products without mechanical training or explicitly forming the full mechanical basis. Across eight three-dimensional optimization benchmarks exceeding one million fine elements each, thermal designs have compliance gaps below 0.3% relative to full finite element method (FEM) reference designs; coupled designs have mixed-objective gaps below 0.027% relative to exact linear-boundary substructure references. Complete coupled optimizations are 4.75–5.05× faster than exact Q1 substructuring in total online time. In separate warmed benchmarks covering states, sensitivities and update proposals, the coupled hybrid gives a 186× speedup over matched Full FEM and reduces peak working-set memory by 94.4%. On a 32 GB laptop, a coupled plate with 30.752 million analysis cells is optimized in 60.54 min using 14.17 GiB peak resident memory. The framework extends reusable local learning from separate-field stiffness approximation to accurate, memory-efficient coupled design.

High-fidelity mechanical data for analyses involving extreme operating conditions are notoriously scarce, as both experimental and numerical simulations are prohibitively expensive. This data bottleneck has limited the efficacy of Generative Artificial Intelligence (GAI) in specialized engineering domains. To address this, the Continuum Mechanics (CM)-GAI theory, a mechanics-informed distribution transport framework that enables the generation of robust mechanical response distributions from limited training datasets, is proposed. By interpreting probability evolution in feature space as the deformation of a continuum body, our method embeds mass-conservation and momentum-balance constraints directly into the transport dynamics. This allows the model to learn complex probability flows with minimal data, yielding accurate predictions across unseen operating regimes, including varied temperatures, strain rates, and impact velocities. The effectiveness of CM-GAI is demonstrated through constitutive law modeling, part-scale thermo-mechanical response prediction, and the transient Taylor rod impact problem. These results confirm that mechanics-informed distribution transport provides a powerful, physics-consistent generative framework for mechanical systems in data-scarce environments.