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

2024-06-23

AI Summary

To address challenges in multiscale microstructure design—including difficulty optimizing fine-scale connectivity and maintaining cross-scale elastic property consistency under computational resource constraints—this work proposes a boundary-consistent active learning paradigm, generating 16 high-quality microstructure datasets spanning a broad range of equivalent elastic moduli. Integrating homogenization theory with physical constraints (periodic boundary conditions and target elasticity tensors), we design a guided diffusion generative model enabling simultaneous control over geometric boundaries and mechanical performance. Furthermore, the model is embedded within a multiscale topology optimization framework to enable macro-micro co-design. Experiments demonstrate that inverse design of mechanical cloaks is accomplished in just one minute, using macro- and micro-grids of 30×30 and 256×256 elements respectively—achieving substantial efficiency gains over prior approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Active Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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, extit{ extbf{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 $30 imes 30$ elements and microstructures filled with $256 imes 256$ elements. The entire reverse design process is completed within one minute, significantly enhancing the efficiency of the multiscale topology optimization.

Problem

• Multi-scale Structure Design
• Computational Efficiency
• Elastic Property Optimization

Innovation

• Guided Diffusion
• Deep Generative Models
• Active Learning Strategy