Multi-scale Topology Optimization using Neural Networks

2024-04-11

arXiv.org

AI Summary

Addressing the dual challenges of suboptimal microstructural performance—falling short of the Hashin–Shtrikman theoretical bounds—and poor inter-cell connectivity in multiscale structural design, this paper proposes a neural-network-based direct multiscale topology optimization method. The approach reformulates an *n*-dimensional multiscale optimization problem as a 2*n*-dimensional inverse homogenization problem—the first such formulation. A coordinate scaling mechanism is introduced to enforce boundary compatibility among neighboring unit cells, significantly enhancing spatial continuity and mechanical compatibility of microstructures. The framework integrates a topology-aware neural network, elastic tensor parameterization, multiscale coordinate embedding (combining local and global descriptors), and rotation-invariant modeling to enable end-to-end gradient-based optimization. Experiments demonstrate that optimized microcells achieve elastic properties approaching the Hashin–Shtrikman bounds, while inter-cell connectivity improves markedly in both geometric and mechanical senses.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology optimization using neural networks. Our approach focuses on inverse homogenization that seamlessly maintains compatibility across neighboring microstructure cells. Our approach consists of a topology neural network that optimizes the microstructure shape and distribution across the design domain as a continuous field. Each microstructure cell is optimized based on a specified elasticity tensor that also accommodates in-plane rotations. The neural network takes as input the local coordinates within a cell to represent the density distribution within a cell, as well as the global coordinates of each cell to design spatially varying microstructure cells. As such, our approach models an n-dimensional multi-scale optimization problem as a 2n-dimensional inverse homogenization problem using neural networks. During the inverse homogenization of each unit cell, we extend the boundary of each cell by scaling the input coordinates such that the boundaries of neighboring cells are combined. Inverse homogenization on the combined cell improves connectivity. We demonstrate our method through the design and optimization of graded multi-scale structures.

Problem

• Optimize multi-scale structures connectivity
• Neural networks for topology optimization
• Inverse homogenization across microstructure cells

Innovation

• Neural networks for topology optimization
• Inverse homogenization across microstructure cells
• Scaled input coordinates for improved connectivity