Style-IH-GAN: diverse inverse homogenization and continuous graded synthesis of cellular metamaterials

Abstract

The inverse design of cellular metamaterials—finding unit-cell geometries that realize prescribed effective properties—is intrinsically one-to-many, yet conditional generators often collapse to narrow outputs and graded assembly can introduce interface discontinuities. We present Style-IH-GAN, a style-modulated generative adversarial network for triply periodic minimal surface (TPMS)-based cellular materials. A mapping network converts latent noise into style vectors that modulate a property-conditioned generator, while mode-seeking and property-consistency losses encourage geometric alternatives under fixed targets. For graded synthesis, the model emits a spatial field of TPMS descriptors in one batched forward pass, and trilinear interpolation supports continuous inter-cell reconstruction. The predictor is used only as a differentiable training signal and controlled baseline metric; unit-cell fidelity is evaluated by numerical homogenization over 750 generated samples across 15 targets. Compared with a vanilla conditional generative adversarial network, Style-IH-GAN achieves 2.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} higher shape-parameter diversity and 19% lower surrogate Young’s modulus error, while a 300-cell graded field is produced in sub-millisecond time. Accuracy remains strongest inside the supported training manifold and requires numerical-homogenization screening; boundary and extrapolated-density targets are reported as limitations. A graded cantilever provides a qualitative macroscopic continuity check.