Generative Inverse Design of Shell Metamaterials through Continuous-Latent Conditional Flow Matching

Abstract Mechanical metamaterials derive programmable properties from a repeated unit cell’s geometry. A stress–strain curve summarizesa three-dimensional shell geometry in a few numbers, so distinct geometries can share a curve and the inversemap from curve to geometry is one-to-many. We develop a continuous-latent conditional flow-matching framework thatdesigns periodic shell unit cells for prescribed compressive responses. Each shell geometry is a continuous periodic function,and a function encoder learns a basis that compresses it into 32 coefficients. Conditional flow matching learns theresponse-conditioned coefficient distribution and generates many candidate geometries. On 200 held-out targets, our 5.9-million-parameter model reaches a mean best-of-20 NRMSE of 0.074 at 73% validity, against 0.118 and 48% for a 40-million-parameter tokenized-diffusion baseline. Sampling requires 26.8 ms per candidate versus 2.03 s for the baseline.Finite-element analysis of 981 shortlisted candidates yields a mean best-design NRMSE of 0.092, compared with a simulationto-simulation reproducibility of 0.016–0.063.