MetaGround: Physics-Grounded Conditional Diffusion for Nonlinear Metamaterial Inverse Design

Generative models for nonlinear metamaterial inverse design are typically confined to a single mechanical property, overlooking the physical coupling between the stress-strain (SS) response and volume fraction (VF). These generators rely on surrogate proxies to rapidly pre-screen candidate geometries, yet evaluating with proxies not validated against physical ground truth produces an optimistic bias that inflates apparent performance, and low-accuracy pre-screening in turn requires more inference candidates for compensation. We present MetaGround, a DBTL-style framework in which conditional diffusion designs SDF candidate geometries, FEM simulation builds physical ground truth, a surrogate proxy tests candidate quality, and residual-guided adaptation learns to recalibrate the proxy. Within this loop, MetaGround introduces multi-physics conditioning architectures for SS and VF, a VF extrapolation protocol probing the generalization boundary, FEM-supervised adaptation driven by residual-guided selection, and finally an independent test set sampled from the full design space to anchor evaluation in FEM ground truth. Experiments show that the cross-attention + FiLM configuration (B2-PD) outperforms the baseline and is the most robust under deep VF extrapolation; the independent test set systematically confirms the optimistic bias of the proxy, and residual-guided selection improves proxy accuracy, raising the downstream screening pass rate from 34.4% to 39.6% at a fixed FEM budget.