Constructing Boundary-identical Microstructures via Guided Diffusion for Fast Multiscale Topology Optimization

TL;DR

This work tackles the challenge of multiscale design where microstructures must share identical boundaries across scales while spanning a wide range of elastic moduli. The authors introduce a self-conditioning diffusion model guided by boundary and homogenized elastic tensors to generate boundary-identical, cubic-symmetric microstructures, and they develop an active learning loop to progressively expand modulus coverage. They construct 16 large-scale datasets and validate that boundary-identical microstructures closely approach Hashin–Shtrikman bounds, enabling fast, accurate multiscale topology optimization—demonstrated on mechanical cloaks and customized displacement designs, with reverse design finished in roughly one minute. The approach significantly accelerates multiscale design workflows and provides a data-driven route to robust, boundary-consistent microstructure libraries for engineering applications.

Abstract

Hierarchical structures exhibit critical features across multiple scales. However, designing multiscale structures demands significant computational resources, and ensuring connectivity between microstructures remains a key challenge. To address these issues, \textit{\textbf{large-range, boundary-identical microstructure datasets}} are successfully constructed, where the microstructures share the same boundaries and exhibit a wide range of elastic moduli. This approach enables highly efficient multiscale topology optimization. Central to our technique adopts a deep generative model, guided diffusion, to generate microstructures under the two conditions, including the specified boundary and homogenized elastic tensor. We generate the desired datasets using active learning approaches, where microstructures with diverse elastic moduli are iteratively added to the dataset, which is then retrained. %We achieve the desired datasets by active learning approaches which are alternately adding microstructures with diverse elastic modulus constructed by the deep generative model into the dataset and retraining the deep generative model. After that, sixteen boundary-identical microstructure datasets with wide ranges of elastic modulus %high property coverage are constructed. We demonstrate the effectiveness and practicability of the obtained datasets over various multiscale design examples. Specifically, in the design of a mechanical cloak, we utilize macrostructures with $30 \times 30$ elements and microstructures filled with $256 \times 256$ elements. The entire reverse design process is completed within one minute, significantly enhancing the efficiency of the multiscale topology optimization.

Figures (21)

• Figure 1: Illustration of boundary connections. (a) The boundary is completely disconnected. (b) The boundary is partly connected. (c) The boundary is fully connected, known as boundary-identical microstructure sets.
• Figure 2: The pipeline of constructing large-range boundary-identical microstructure datasets and their applications. (a) The cubic symmetric microstructure dataset without identical boundaries. (b) Representative boundaries derived from boundary clustering. (c) Generated microstructure datasets with the specified boundaries, which are expanded through guided diffusion and active learning. (d) A dataset with a wide range of elastic moduli. (e)-(f) The results of multiscale topology optimization.
• Figure 3: Plots of $C_{11}$ vs. $C_{12}/C_{11}$ (a) and $C_{11}$ vs. $C_{33}$ (b) on a cubic symmetric microstructure dataset $\mathcal{D}_0$ without identical boundaries. The number of microstructures is 36,585.
• Figure 4: Illustration of sixteen boundaries derived by k-means clustering in dataset $\mathcal{D}_0$. Green boundaries indicate that there are corresponding boundaries in $\mathcal{D}_0$, while yellow boundaries indicate that no microstructures with these boundaries are found in $\mathcal{D}_0$.
• Figure 5: Network architecture of the proposed self-conditioning diffusion model.