MIND: Microstructure INverse Design with Generative Hybrid Neural Representation

TL;DR

MIND tackles the inverse design of 3D tileable metamaterial microstructures by unifying geometry and physics in a Holoplane latent space and driving generation with a diffusion model conditioned on target elastic properties. The approach introduces a symmetry-aware, physics-informed hybrid representation and boundary-aware diffusion sampling to produce diverse, geometrically valid structures that closely match target tensors while enabling heterogeneous tiling. With a large multi-class dataset and comprehensive experiments, MIND demonstrates state-of-the-art property accuracy, improved boundary compatibility, and capabilities in interpolation, infilling, and printable designs, including complex assemblies. The framework offers a flexible, open-source pipeline for rapid, property-driven metamaterial design across multiple microstructure classes, potentially accelerating practical adoption in additive manufacturing and beyond.

Abstract

The inverse design of microstructures plays a pivotal role in optimizing metamaterials with specific, targeted physical properties. While traditional forward design methods are constrained by their inability to explore the vast combinatorial design space, inverse design offers a compelling alternative by directly generating structures that fulfill predefined performance criteria. However, achieving precise control over both geometry and material properties remains a significant challenge due to their intricate interdependence. Existing approaches, which typically rely on voxel or parametric representations, often limit design flexibility and structural diversity. In this work, we present a novel generative model that integrates latent diffusion with Holoplane, an advanced hybrid neural representation that simultaneously encodes both geometric and physical properties. This combination ensures superior alignment between geometry and properties. Our approach generalizes across multiple microstructure classes, enabling the generation of diverse, tileable microstructures with significantly improved property accuracy and enhanced control over geometric validity, surpassing the performance of existing methods. We introduce a multi-class dataset encompassing a variety of geometric morphologies, including truss, shell, tube, and plate structures, to train and validate our model. Experimental results demonstrate the model's ability to generate microstructures that meet target properties, maintain geometric validity, and integrate seamlessly into complex assemblies. Additionally, we explore the potential of our framework through the generation of new microstructures, cross-class interpolation, and the infilling of heterogeneous microstructures. The dataset and source code will be open-sourced upon publication.

Figures (13)

• Figure 1: Pipeline of the MIND. (a) We explicitly encode the microstructural symmetry in voxel space, leveraging the inherent symmetry to ensure tilability. (b) A combination of distance and displacement fields integrates physical priors into the implicit fields, enabling a hybrid neural representation, Holoplane. (c) Holoplane can be conditionally generated using a diffusion model, yielding diverse microstructural demands. (d) We apply this process to heterogeneous design, generating seamlessly fitting, 3D-printable structures.
• Figure 2: Left: Resolution 128, Right: Super-resolution 196.
• Figure 3: We visualize the latent space with and without physical priors using t-SNE. The color represents Young's moduli. Without physical priors, close data points exhibit significant property discrepancies (a). This disordered latent space (b) hinders the Diffusion model's ability to condition effectively. Incorporating physical priors improves this distribution significantly (c). We further conducted ablation experiments to compare the results of using the generative model in space (b) and (c) (Sec.\ref{['sec:accuracy']}).
• Figure 4: We enhance the boundary compatibility through smooth interpolation. (a) The blended microstructure’s SDF is decoded from the corresponding positions in the interpolation sequence. We quantify boundary similarity using the intersection-over-union (IoU) of binarized boundary surfaces. (b) Using only the boundary compatibility gradient, we achieve 70.1% boundary similarity. (c) Under blending, boundary compatibility reaches 100%.
• Figure 5: Exemplar models for four different structure types.