HyperDiff: An Inverse Design Framework for Hyperelastic Microstructures Based on a Conditional Diffusion Model

Design: ing hyperelastic porous microstructures under finite strain is challenging because bending, buckling, contact, and densification interact to produce nonconvex and one-to-many relations 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, providing temporal and mechanical context that guides the denoising process toward physically consistent configurations with the desired multi-stage 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 (bending-buckling-densification) 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, yet the framework is extensible to 3D, multi-resolution, and multi-physics systems. By combining physics-aware conditioning with generative sampling, HyperDiff establishes a practical front end for mechanics-based design workflows, applicable to programmable soft actuators, impact-energy absorbers with tunable plateaus, and rapid exploration of nonlinear architected materials for soft and deformable systems.